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import ECTate.Algebra.EllipticCurve.Kronecker
import ECTate.Algebra.EllipticCurve.Model
import ECTate.Algebra.EllipticCurve.ValuedRing
import ECTate.Data.Nat.Enat
import Mathlib.Init.Data.Int.Basic
import Mathlib.Tactic.LibrarySearch
import Mathlib.Tactic.NormNum
import Mathlib.Tactic.Contrapose

open Enat

variable {
R: Type u
R
:
Type u: Type (u + 1)
Type u
} [inst :
IntegralDomain: Type ?u.13188Type ?u.13188
IntegralDomain
R: Type u
R
] namespace Model variable {
p: R
p
:
R: Type u
R
} def
is_local_singular_point: {R : Type u} → [inst : IntegralDomain R] → {p : R} → SurjVal pModel RR × RProp
is_local_singular_point
(
valp: SurjVal p
valp
:
SurjVal: {R : Type ?u.21} → R[inst : IntegralDomain R] → Type ?u.21
SurjVal
p: R
p
) (
e: Model R
e
:
Model: (R : Type ?u.29) → [inst : IntegralDomain R] → Type ?u.29
Model
R: Type u
R
) (
P: R × R
P
:
R: Type u
R
×
R: Type u
R
) :
Prop: Type
Prop
:=
valp: SurjVal p
valp
.
v: {R : Type ?u.42} → {p : R} → [inst : IntegralDomain R] → SurjVal pRℕ∪∞
v
(
weierstrass: {R : Type ?u.49} → [inst : IntegralDomain R] → Model RR × RR
weierstrass
e: Model R
e
P: R × R
P
) >
0: ?m.57
0
valp: SurjVal p
valp
.
v: {R : Type ?u.296} → {p : R} → [inst : IntegralDomain R] → SurjVal pRℕ∪∞
v
(
dweierstrass_dx: {R : Type ?u.300} → [inst : IntegralDomain R] → Model RR × RR
dweierstrass_dx
e: Model R
e
P: R × R
P
) >
0: ?m.304
0
valp: SurjVal p
valp
.
v: {R : Type ?u.322} → {p : R} → [inst : IntegralDomain R] → SurjVal pRℕ∪∞
v
(
dweierstrass_dy: {R : Type ?u.326} → [inst : IntegralDomain R] → Model RR × RR
dweierstrass_dy
e: Model R
e
P: R × R
P
) >
0: ?m.330
0
lemma
Warning: declaration uses 'sorry'
(
valp: SurjVal p
valp
:
SurjVal: {R : Type ?u.367} → R[inst : IntegralDomain R] → Type ?u.367
SurjVal
p: R
p
) (
e: Model R
e
:
Model: (R : Type ?u.375) → [inst : IntegralDomain R] → Type ?u.375
Model
R: Type u
R
) (
h: SurjVal.v valp (discr e) > 0
h
:
valp: SurjVal p
valp
.
v: {R : Type ?u.380} → {p : R} → [inst : IntegralDomain R] → SurjVal pRℕ∪∞
v
e: Model R
e
.
discr: {R : Type ?u.387} → [inst : IntegralDomain R] → Model RR
discr
>
0: ?m.396
0
) : ∃
P: ?m.639
P
,
is_local_singular_point: {R : Type ?u.641} → [inst : IntegralDomain R] → {p : R} → SurjVal pModel RR × RProp
is_local_singular_point
valp: SurjVal p
valp
e: Model R
e
P: ?m.639
P
:=
R: Type u

inst: IntegralDomain R

p: R

valp: SurjVal p

e: Model R

h: SurjVal.v valp (discr e) > 0


P, is_local_singular_point valp e P

Goals accomplished! 🐙
def
move_singular_point_to_origin_triple: {R : Type u} → [inst : IntegralDomain R] → {p : R} → EnatValRing pModel RR × R × R
move_singular_point_to_origin_triple
(evr :
EnatValRing: {R : Type ?u.675} → R[inst : IntegralDomain R] → Type ?u.675
EnatValRing
p: R
p
) (
e: Model R
e
:
Model: (R : Type ?u.683) → [inst : IntegralDomain R] → Type ?u.683
Model
R: Type u
R
) :
R: Type u
R
×
R: Type u
R
×
R: Type u
R
:= match evr.
residue_char: {R : Type ?u.701} → {p : R} → [inst : IntegralDomain R] → EnatValRing p
residue_char
with |
2:
2
=> (evr.
norm_repr: {R : Type ?u.725} → {p : R} → [inst : IntegralDomain R] → EnatValRing pRR
norm_repr
e: Model R
e
.
a4: {R : Type ?u.729} → [inst : IntegralDomain R] → Model RR
a4
,
0: ?m.739
0
, evr.
norm_repr: {R : Type ?u.790} → {p : R} → [inst : IntegralDomain R] → EnatValRing pRR
norm_repr
(
e: Model R
e
.
a6: {R : Type ?u.797} → [inst : IntegralDomain R] → Model RR
a6
+
e: Model R
e
.
a4: {R : Type ?u.803} → [inst : IntegralDomain R] → Model RR
a4
*
e: Model R
e
.
a2: {R : Type ?u.806} → [inst : IntegralDomain R] → Model RR
a2
)) |
3:
3
=> (evr.
norm_repr: {R : Type ?u.989} → {p : R} → [inst : IntegralDomain R] → EnatValRing pRR
norm_repr
(-
e: Model R
e
.
b6: {R : Type ?u.994} → [inst : IntegralDomain R] → Model RR
b6
),
0: ?m.1023
0
, evr.
norm_repr: {R : Type ?u.1025} → {p : R} → [inst : IntegralDomain R] → EnatValRing pRR
norm_repr
(
e: Model R
e
.
a3: {R : Type ?u.1032} → [inst : IntegralDomain R] → Model RR
a3
-
e: Model R
e
.
b6: {R : Type ?u.1038} → [inst : IntegralDomain R] → Model RR
b6
*
e: Model R
e
.
a1: {R : Type ?u.1044} → [inst : IntegralDomain R] → Model RR
a1
)) | _ => (
0: ?m.1154
0
,
0: ?m.1161
0
,
0: ?m.1164
0
) --need to fill here def
move_singular_point_to_origin_iso: EnatValRing pModel RModel R
move_singular_point_to_origin_iso
(evr :
EnatValRing: {R : Type ?u.1931} → R[inst : IntegralDomain R] → Type ?u.1931
EnatValRing
p: R
p
) (
e: Model R
e
:
Model: (R : Type ?u.1939) → [inst : IntegralDomain R] → Type ?u.1939
Model
R: Type u
R
) :
Model: (R : Type ?u.1943) → [inst : IntegralDomain R] → Type ?u.1943
Model
R: Type u
R
:=
rst_triple: {R : Type ?u.1948} → [inst : IntegralDomain R] → Model RR × R × RModel R
rst_triple
e: Model R
e
(
move_singular_point_to_origin_triple: {R : Type ?u.1953} → [inst : IntegralDomain R] → {p : R} → EnatValRing pModel RR × R × R
move_singular_point_to_origin_triple
evr
e: Model R
e
) lemma
Warning: declaration uses 'sorry'
(evr :
EnatValRing: {R : Type ?u.2013} → R[inst : IntegralDomain R] → Type ?u.2013
EnatValRing
p: R
p
) (
e: Model R
e
:
Model: (R : Type ?u.2021) → [inst : IntegralDomain R] → Type ?u.2021
Model
R: Type u
R
) : (∃
P: ?m.2052
P
,
is_local_singular_point: {R : Type ?u.2054} → [inst : IntegralDomain R] → {p : R} → SurjVal pModel RR × RProp
is_local_singular_point
valp: ?m.2036
valp
e: Model R
e
P: ?m.2052
P
) →
is_local_singular_point: {R : Type ?u.2073} → [inst : IntegralDomain R] → {p : R} → SurjVal pModel RR × RProp
is_local_singular_point
valp: ?m.2036
valp
(
move_singular_point_to_origin_iso: {R : Type ?u.2083} → [inst : IntegralDomain R] → {p : R} → EnatValRing pModel RModel R
move_singular_point_to_origin_iso
evr
e: Model R
e
) (
0: ?m.2095
0
,
0: ?m.2147
0
) :=
R: Type u

inst: IntegralDomain R

p, p✝: R

valp: SurjVal p✝

evr: EnatValRing p

e: Model R



Goals accomplished! 🐙
def
pi_scaling: EnatValRing pModel RModel R
pi_scaling
(evr :
EnatValRing: {R : Type ?u.2185} → R[inst : IntegralDomain R] → Type ?u.2185
EnatValRing
p: R
p
) (
e: Model R
e
:
Model: (R : Type ?u.2193) → [inst : IntegralDomain R] → Type ?u.2193
Model
R: Type u
R
) :
Model: (R : Type ?u.2197) → [inst : IntegralDomain R] → Type ?u.2197
Model
R: Type u
R
:= { a1 := evr.
sub_val: {R : Type ?u.2207} → [inst : IntegralDomain R] → {p : R} → EnatValRing pRR
sub_val
e: Model R
e
.
a1: {R : Type ?u.2220} → [inst : IntegralDomain R] → Model RR
a1
1: ?m.2224
1
, a2 := evr.
sub_val: {R : Type ?u.2234} → [inst : IntegralDomain R] → {p : R} → EnatValRing pRR
sub_val
e: Model R
e
.
a2: {R : Type ?u.2244} → [inst : IntegralDomain R] → Model RR
a2
2: ?m.2248
2
, a3 := evr.
sub_val: {R : Type ?u.2253} → [inst : IntegralDomain R] → {p : R} → EnatValRing pRR
sub_val
e: Model R
e
.
a3: {R : Type ?u.2263} → [inst : IntegralDomain R] → Model RR
a3
3: ?m.2267
3
, a4 := evr.
sub_val: {R : Type ?u.2272} → [inst : IntegralDomain R] → {p : R} → EnatValRing pRR
sub_val
e: Model R
e
.
a4: {R : Type ?u.2282} → [inst : IntegralDomain R] → Model RR
a4
4: ?m.2286
4
, a6 := evr.
sub_val: {R : Type ?u.2291} → [inst : IntegralDomain R] → {p : R} → EnatValRing pRR
sub_val
e: Model R
e
.
a6: {R : Type ?u.2301} → [inst : IntegralDomain R] → Model RR
a6
6: ?m.2305
6
} lemma
pi_scaling_of_b2: ∀ {R : Type u} [inst : IntegralDomain R] {p : R} (evr : EnatValRing p) (e : Model R), SurjVal.v evr.valtn e.a1 ofN 1SurjVal.v evr.valtn e.a2 ofN 2EnatValRing.sub_val evr (b2 e) 2 = EnatValRing.sub_val evr e.a1 1 * EnatValRing.sub_val evr e.a1 1 + 4 * EnatValRing.sub_val evr e.a2 2
pi_scaling_of_b2
(evr :
EnatValRing: {R : Type ?u.2390} → R[inst : IntegralDomain R] → Type ?u.2390
EnatValRing
p: R
p
) (
e: Model R
e
:
Model: (R : Type ?u.2398) → [inst : IntegralDomain R] → Type ?u.2398
Model
R: Type u
R
) (
h1: SurjVal.v evr.valtn e.a1 ofN 1
h1
: evr.
valtn: {R : Type ?u.2403} → {p : R} → [inst : IntegralDomain R] → EnatValRing pSurjVal p
valtn
.
v: {R : Type ?u.2410} → {p : R} → [inst : IntegralDomain R] → SurjVal pRℕ∪∞
v
e: Model R
e
.
a1: {R : Type ?u.2417} → [inst : IntegralDomain R] → Model RR
a1
ofN: ℕ∪∞
ofN
1: ?m.2423
1
) (
h2: SurjVal.v evr.valtn e.a2 ofN 2
h2
: evr.
valtn: {R : Type ?u.2441} → {p : R} → [inst : IntegralDomain R] → EnatValRing pSurjVal p
valtn
.
v: {R : Type ?u.2445} → {p : R} → [inst : IntegralDomain R] → SurjVal pRℕ∪∞
v
e: Model R
e
.
a2: {R : Type ?u.2449} → [inst : IntegralDomain R] → Model RR
a2
ofN: ℕ∪∞
ofN
2: ?m.2453
2
) : evr.
sub_val: {R : Type ?u.2463} → [inst : IntegralDomain R] → {p : R} → EnatValRing pRR
sub_val
e: Model R
e
.
b2: {R : Type ?u.2473} → [inst : IntegralDomain R] → Model RR
b2
2: ?m.2480
2
= evr.
sub_val: {R : Type ?u.2488} → [inst : IntegralDomain R] → {p : R} → EnatValRing pRR
sub_val
e: Model R
e
.
a1: {R : Type ?u.2498} → [inst : IntegralDomain R] → Model RR
a1
1: ?m.2502
1
* evr.
sub_val: {R : Type ?u.2504} → [inst : IntegralDomain R] → {p : R} → EnatValRing pRR
sub_val
e: Model R
e
.
a1: {R : Type ?u.2514} → [inst : IntegralDomain R] → Model RR
a1
1: ?m.2518
1
+
4: ?m.2524
4
* evr.
sub_val: {R : Type ?u.2533} → [inst : IntegralDomain R] → {p : R} → EnatValRing pRR
sub_val
e: Model R
e
.
a2: {R : Type ?u.2543} → [inst : IntegralDomain R] → Model RR
a2
2: ?m.2547
2
:=
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2


R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2


R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2


EnatValRing.sub_val evr (b2 e) 2 = EnatValRing.sub_val evr (EnatValRing.sub_val evr e.a1 1 * e.a1) 1 + 4 * EnatValRing.sub_val evr e.a2 2
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2


R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2


EnatValRing.sub_val evr (b2 e) 2 = EnatValRing.sub_val evr (EnatValRing.sub_val evr (e.a1 * e.a1) 1) 1 + 4 * EnatValRing.sub_val evr e.a2 2
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2


R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2


EnatValRing.sub_val evr (b2 e) 2 = EnatValRing.sub_val evr (e.a1 * e.a1) (1 + 1) + 4 * EnatValRing.sub_val evr e.a2 2
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2


R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2


EnatValRing.sub_val evr (b2 e) 2 = EnatValRing.sub_val evr (e.a1 * e.a1) (1 + 1) + EnatValRing.sub_val evr (4 * e.a2) 2
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2


R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2


EnatValRing.sub_val evr (b2 e) 2 = EnatValRing.sub_val evr (e.a1 * e.a1 + 4 * e.a2) (1 + 1)
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2


SurjVal.v evr.valtn (e.a1 * e.a1) ofN (1 + 1)
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2


SurjVal.v evr.valtn (4 * e.a2) ofN (1 + 1)
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2


EnatValRing.sub_val evr (b2 e) 2 = EnatValRing.sub_val evr (e.a1 * e.a1 + 4 * e.a2) (1 + 1)
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2


SurjVal.v evr.valtn (e.a1 * e.a1) ofN (1 + 1)
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2


SurjVal.v evr.valtn (4 * e.a2) ofN (1 + 1)
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2


R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2


EnatValRing.sub_val evr (b2 e) 2 = EnatValRing.sub_val evr (e.a1 * e.a1 + 4 * e.a2) (1 + 1)
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2


EnatValRing.sub_val evr (b2 e) 2 = EnatValRing.sub_val evr (e.a1 * e.a1 + 4 * e.a2) (1 + 1)
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2


SurjVal.v evr.valtn (e.a1 * e.a1) ofN (1 + 1)
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2


SurjVal.v evr.valtn (4 * e.a2) ofN (1 + 1)

Goals accomplished! 🐙
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2


R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2


SurjVal.v evr.valtn (e.a1 * e.a1) ofN (1 + 1)
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2


SurjVal.v evr.valtn (e.a1 * e.a1) ofN (1 + 1)
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2


SurjVal.v evr.valtn (4 * e.a2) ofN (1 + 1)

Goals accomplished! 🐙
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2


R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2


SurjVal.v evr.valtn (4 * e.a2) ofN (1 + 1)
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2


SurjVal.v evr.valtn (4 * e.a2) ofN (1 + 1)

Goals accomplished! 🐙
lemma
pi_scaling_of_b4: ∀ (evr : EnatValRing p) (e : Model R), SurjVal.v evr.valtn e.a1 ofN 1SurjVal.v evr.valtn e.a3 ofN 3SurjVal.v evr.valtn e.a4 ofN 4EnatValRing.sub_val evr (b4 e) 4 = EnatValRing.sub_val evr e.a1 1 * EnatValRing.sub_val evr e.a3 3 + 2 * EnatValRing.sub_val evr e.a4 4
pi_scaling_of_b4
(evr :
EnatValRing: {R : Type ?u.3120} → R[inst : IntegralDomain R] → Type ?u.3120
EnatValRing
p: R
p
) (
e: Model R
e
:
Model: (R : Type ?u.3128) → [inst : IntegralDomain R] → Type ?u.3128
Model
R: Type u
R
) (
h1: SurjVal.v evr.valtn e.a1 ofN 1
h1
: evr.
valtn: {R : Type ?u.3133} → {p : R} → [inst : IntegralDomain R] → EnatValRing pSurjVal p
valtn
.
v: {R : Type ?u.3140} → {p : R} → [inst : IntegralDomain R] → SurjVal pRℕ∪∞
v
e: Model R
e
.
a1: {R : Type ?u.3147} → [inst : IntegralDomain R] → Model RR
a1
ofN: ℕ∪∞
ofN
1: ?m.3153
1
) (
h3: SurjVal.v evr.valtn e.a3 ofN 3
h3
: evr.
valtn: {R : Type ?u.3171} → {p : R} → [inst : IntegralDomain R] → EnatValRing pSurjVal p
valtn
.
v: {R : Type ?u.3175} → {p : R} → [inst : IntegralDomain R] → SurjVal pRℕ∪∞
v
e: Model R
e
.
a3: {R : Type ?u.3179} → [inst : IntegralDomain R] → Model RR
a3
ofN: ℕ∪∞
ofN
3: ?m.3183
3
) (
h4: SurjVal.v evr.valtn e.a4 ofN 4
h4
: evr.
valtn: {R : Type ?u.3193} → {p : R} → [inst : IntegralDomain R] → EnatValRing pSurjVal p
valtn
.
v: {R : Type ?u.3197} → {p : R} → [inst : IntegralDomain R] → SurjVal pRℕ∪∞
v
e: Model R
e
.
a4: {R : Type ?u.3201} → [inst : IntegralDomain R] → Model RR
a4
ofN: ℕ∪∞
ofN
4: ?m.3205
4
) : evr.
sub_val: {R : Type ?u.3215} → [inst : IntegralDomain R] → {p : R} → EnatValRing pRR
sub_val
e: Model R
e
.
b4: {R : Type ?u.3225} → [inst : IntegralDomain R] → Model RR
b4
4: ?m.3232
4
= evr.
sub_val: {R : Type ?u.3240} → [inst : IntegralDomain R] → {p : R} → EnatValRing pRR
sub_val
e: Model R
e
.
a1: {R : Type ?u.3250} → [inst : IntegralDomain R] → Model RR
a1
1: ?m.3254
1
* evr.
sub_val: {R : Type ?u.3256} → [inst : IntegralDomain R] → {p : R} → EnatValRing pRR
sub_val
e: Model R
e
.
a3: {R : Type ?u.3266} → [inst : IntegralDomain R] → Model RR
a3
3: ?m.3270
3
+
2: ?m.3276
2
* evr.
sub_val: {R : Type ?u.3285} → [inst : IntegralDomain R] → {p : R} → EnatValRing pRR
sub_val
e: Model R
e
.
a4: {R : Type ?u.3295} → [inst : IntegralDomain R] → Model RR
a4
4: ?m.3299
4
:=
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4


R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4


R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4


EnatValRing.sub_val evr (b4 e) 4 = EnatValRing.sub_val evr (EnatValRing.sub_val evr e.a1 1 * e.a3) 3 + 2 * EnatValRing.sub_val evr e.a4 4
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4


R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4


EnatValRing.sub_val evr (b4 e) 4 = EnatValRing.sub_val evr (EnatValRing.sub_val evr (e.a1 * e.a3) 1) 3 + 2 * EnatValRing.sub_val evr e.a4 4
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4


R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4


EnatValRing.sub_val evr (b4 e) 4 = EnatValRing.sub_val evr (e.a1 * e.a3) (1 + 3) + 2 * EnatValRing.sub_val evr e.a4 4
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4


R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4


EnatValRing.sub_val evr (b4 e) 4 = EnatValRing.sub_val evr (e.a1 * e.a3) (1 + 3) + EnatValRing.sub_val evr (2 * e.a4) 4
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4


R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4


EnatValRing.sub_val evr (b4 e) 4 = EnatValRing.sub_val evr (e.a1 * e.a3 + 2 * e.a4) (1 + 3)
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4


SurjVal.v evr.valtn (e.a1 * e.a3) ofN (1 + 3)
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4


SurjVal.v evr.valtn (2 * e.a4) ofN (1 + 3)
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4


EnatValRing.sub_val evr (b4 e) 4 = EnatValRing.sub_val evr (e.a1 * e.a3 + 2 * e.a4) (1 + 3)
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4


SurjVal.v evr.valtn (e.a1 * e.a3) ofN (1 + 3)
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4


SurjVal.v evr.valtn (2 * e.a4) ofN (1 + 3)
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4


R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4


EnatValRing.sub_val evr (b4 e) 4 = EnatValRing.sub_val evr (e.a1 * e.a3 + 2 * e.a4) (1 + 3)
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4


EnatValRing.sub_val evr (b4 e) 4 = EnatValRing.sub_val evr (e.a1 * e.a3 + 2 * e.a4) (1 + 3)
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4


SurjVal.v evr.valtn (e.a1 * e.a3) ofN (1 + 3)
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4


SurjVal.v evr.valtn (2 * e.a4) ofN (1 + 3)

Goals accomplished! 🐙
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4


R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4


SurjVal.v evr.valtn (e.a1 * e.a3) ofN (1 + 3)
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4


SurjVal.v evr.valtn (e.a1 * e.a3) ofN (1 + 3)
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4


SurjVal.v evr.valtn (2 * e.a4) ofN (1 + 3)

Goals accomplished! 🐙
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4


R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4


SurjVal.v evr.valtn (2 * e.a4) ofN (1 + 3)
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4


SurjVal.v evr.valtn (2 * e.a4) ofN (1 + 3)

Goals accomplished! 🐙
lemma
pi_scaling_of_b6: ∀ (evr : EnatValRing p) (e : Model R), SurjVal.v evr.valtn e.a3 ofN 3SurjVal.v evr.valtn e.a6 ofN 6EnatValRing.sub_val evr (b6 e) 6 = EnatValRing.sub_val evr e.a3 3 * EnatValRing.sub_val evr e.a3 3 + 4 * EnatValRing.sub_val evr e.a6 6
pi_scaling_of_b6
(evr :
EnatValRing: {R : Type ?u.3874} → R[inst : IntegralDomain R] → Type ?u.3874
EnatValRing
p: R
p
) (
e: Model R
e
:
Model: (R : Type ?u.3882) → [inst : IntegralDomain R] → Type ?u.3882
Model
R: Type u
R
) (
h3: SurjVal.v evr.valtn e.a3 ofN 3
h3
: evr.
valtn: {R : Type ?u.3887} → {p : R} → [inst : IntegralDomain R] → EnatValRing pSurjVal p
valtn
.
v: {R : Type ?u.3894} → {p : R} → [inst : IntegralDomain R] → SurjVal pRℕ∪∞
v
e: Model R
e
.
a3: {R : Type ?u.3901} → [inst : IntegralDomain R] → Model RR
a3
ofN: ℕ∪∞
ofN
3: ?m.3907
3
) (
h6: SurjVal.v evr.valtn e.a6 ofN 6
h6
: evr.
valtn: {R : Type ?u.3924} → {p : R} → [inst : IntegralDomain R] → EnatValRing pSurjVal p
valtn
.
v: {R : Type ?u.3928} → {p : R} → [inst : IntegralDomain R] → SurjVal pRℕ∪∞
v
e: Model R
e
.
a6: {R : Type ?u.3932} → [inst : IntegralDomain R] → Model RR
a6
ofN: ℕ∪∞
ofN
6: ?m.3936
6
) : evr.
sub_val: {R : Type ?u.3946} → [inst : IntegralDomain R] → {p : R} → EnatValRing pRR
sub_val
e: Model R
e
.
b6: {R : Type ?u.3956} → [inst : IntegralDomain R] → Model RR
b6
6: ?m.3963
6
= evr.
sub_val: {R : Type ?u.3971} → [inst : IntegralDomain R] → {p : R} → EnatValRing pRR
sub_val
e: Model R
e
.
a3: {R : Type ?u.3981} → [inst : IntegralDomain R] → Model RR
a3
3: ?m.3985
3
* evr.
sub_val: {R : Type ?u.3987} → [inst : IntegralDomain R] → {p : R} → EnatValRing pRR
sub_val
e: Model R
e
.
a3: {R : Type ?u.3997} → [inst : IntegralDomain R] → Model RR
a3
3: ?m.4001
3
+
4: ?m.4007
4
* evr.
sub_val: {R : Type ?u.4016} → [inst : IntegralDomain R] → {p : R} → EnatValRing pRR
sub_val
e: Model R
e
.
a6: {R : Type ?u.4026} → [inst : IntegralDomain R] → Model RR
a6
6: ?m.4030
6
:=
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h3: SurjVal.v evr.valtn e.a3 ofN 3

h6: SurjVal.v evr.valtn e.a6 ofN 6


R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h3: SurjVal.v evr.valtn e.a3 ofN 3

h6: SurjVal.v evr.valtn e.a6 ofN 6


R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h3: SurjVal.v evr.valtn e.a3 ofN 3

h6: SurjVal.v evr.valtn e.a6 ofN 6


EnatValRing.sub_val evr (b6 e) 6 = EnatValRing.sub_val evr (EnatValRing.sub_val evr e.a3 3 * e.a3) 3 + 4 * EnatValRing.sub_val evr e.a6 6
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h3: SurjVal.v evr.valtn e.a3 ofN 3

h6: SurjVal.v evr.valtn e.a6 ofN 6


R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h3: SurjVal.v evr.valtn e.a3 ofN 3

h6: SurjVal.v evr.valtn e.a6 ofN 6


EnatValRing.sub_val evr (b6 e) 6 = EnatValRing.sub_val evr (EnatValRing.sub_val evr (e.a3 * e.a3) 3) 3 + 4 * EnatValRing.sub_val evr e.a6 6
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h3: SurjVal.v evr.valtn e.a3 ofN 3

h6: SurjVal.v evr.valtn e.a6 ofN 6


R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h3: SurjVal.v evr.valtn e.a3 ofN 3

h6: SurjVal.v evr.valtn e.a6 ofN 6


EnatValRing.sub_val evr (b6 e) 6 = EnatValRing.sub_val evr (e.a3 * e.a3) (3 + 3) + 4 * EnatValRing.sub_val evr e.a6 6
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h3: SurjVal.v evr.valtn e.a3 ofN 3

h6: SurjVal.v evr.valtn e.a6 ofN 6


R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h3: SurjVal.v evr.valtn e.a3 ofN 3

h6: SurjVal.v evr.valtn e.a6 ofN 6


EnatValRing.sub_val evr (b6 e) 6 = EnatValRing.sub_val evr (e.a3 * e.a3) (3 + 3) + EnatValRing.sub_val evr (4 * e.a6) 6
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h3: SurjVal.v evr.valtn e.a3 ofN 3

h6: SurjVal.v evr.valtn e.a6 ofN 6


R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h3: SurjVal.v evr.valtn e.a3 ofN 3

h6: SurjVal.v evr.valtn e.a6 ofN 6


EnatValRing.sub_val evr (b6 e) 6 = EnatValRing.sub_val evr (e.a3 * e.a3 + 4 * e.a6) (3 + 3)
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h3: SurjVal.v evr.valtn e.a3 ofN 3

h6: SurjVal.v evr.valtn e.a6 ofN 6


SurjVal.v evr.valtn (e.a3 * e.a3) ofN (3 + 3)
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h3: SurjVal.v evr.valtn e.a3 ofN 3

h6: SurjVal.v evr.valtn e.a6 ofN 6


SurjVal.v evr.valtn (4 * e.a6) ofN (3 + 3)
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h3: SurjVal.v evr.valtn e.a3 ofN 3

h6: SurjVal.v evr.valtn e.a6 ofN 6


EnatValRing.sub_val evr (b6 e) 6 = EnatValRing.sub_val evr (e.a3 * e.a3 + 4 * e.a6) (3 + 3)
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h3: SurjVal.v evr.valtn e.a3 ofN 3

h6: SurjVal.v evr.valtn e.a6 ofN 6


SurjVal.v evr.valtn (e.a3 * e.a3) ofN (3 + 3)
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h3: SurjVal.v evr.valtn e.a3 ofN 3

h6: SurjVal.v evr.valtn e.a6 ofN 6


SurjVal.v evr.valtn (4 * e.a6) ofN (3 + 3)
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h3: SurjVal.v evr.valtn e.a3 ofN 3

h6: SurjVal.v evr.valtn e.a6 ofN 6


R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h3: SurjVal.v evr.valtn e.a3 ofN 3

h6: SurjVal.v evr.valtn e.a6 ofN 6


EnatValRing.sub_val evr (b6 e) 6 = EnatValRing.sub_val evr (e.a3 * e.a3 + 4 * e.a6) (3 + 3)
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h3: SurjVal.v evr.valtn e.a3 ofN 3

h6: SurjVal.v evr.valtn e.a6 ofN 6


EnatValRing.sub_val evr (b6 e) 6 = EnatValRing.sub_val evr (e.a3 * e.a3 + 4 * e.a6) (3 + 3)
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h3: SurjVal.v evr.valtn e.a3 ofN 3

h6: SurjVal.v evr.valtn e.a6 ofN 6


SurjVal.v evr.valtn (e.a3 * e.a3) ofN (3 + 3)
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h3: SurjVal.v evr.valtn e.a3 ofN 3

h6: SurjVal.v evr.valtn e.a6 ofN 6


SurjVal.v evr.valtn (4 * e.a6) ofN (3 + 3)

Goals accomplished! 🐙
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h3: SurjVal.v evr.valtn e.a3 ofN 3

h6: SurjVal.v evr.valtn e.a6 ofN 6


R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h3: SurjVal.v evr.valtn e.a3 ofN 3

h6: SurjVal.v evr.valtn e.a6 ofN 6


SurjVal.v evr.valtn (e.a3 * e.a3) ofN (3 + 3)
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h3: SurjVal.v evr.valtn e.a3 ofN 3

h6: SurjVal.v evr.valtn e.a6 ofN 6


SurjVal.v evr.valtn (e.a3 * e.a3) ofN (3 + 3)
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h3: SurjVal.v evr.valtn e.a3 ofN 3

h6: SurjVal.v evr.valtn e.a6 ofN 6


SurjVal.v evr.valtn (4 * e.a6) ofN (3 + 3)

Goals accomplished! 🐙
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h3: SurjVal.v evr.valtn e.a3 ofN 3

h6: SurjVal.v evr.valtn e.a6 ofN 6


R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h3: SurjVal.v evr.valtn e.a3 ofN 3

h6: SurjVal.v evr.valtn e.a6 ofN 6


SurjVal.v evr.valtn (4 * e.a6) ofN (3 + 3)
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h3: SurjVal.v evr.valtn e.a3 ofN 3

h6: SurjVal.v evr.valtn e.a6 ofN 6


SurjVal.v evr.valtn (4 * e.a6) ofN (3 + 3)

Goals accomplished! 🐙
lemma
pi_scaling_of_b8: ∀ (evr : EnatValRing p) (e : Model R), SurjVal.v evr.valtn e.a1 ofN 1SurjVal.v evr.valtn e.a2 ofN 2SurjVal.v evr.valtn e.a3 ofN 3SurjVal.v evr.valtn e.a4 ofN 4SurjVal.v evr.valtn e.a6 ofN 6EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr e.a1 1 * EnatValRing.sub_val evr e.a1 1 * EnatValRing.sub_val evr e.a6 6 - EnatValRing.sub_val evr e.a1 1 * EnatValRing.sub_val evr e.a3 3 * EnatValRing.sub_val evr e.a4 4 + 4 * EnatValRing.sub_val evr e.a2 2 * EnatValRing.sub_val evr e.a6 6 + EnatValRing.sub_val evr e.a2 2 * EnatValRing.sub_val evr e.a3 3 * EnatValRing.sub_val evr e.a3 3 - EnatValRing.sub_val evr e.a4 4 * EnatValRing.sub_val evr e.a4 4
pi_scaling_of_b8
(evr :
EnatValRing: {R : Type ?u.4603} → R[inst : IntegralDomain R] → Type ?u.4603
EnatValRing
p: R
p
) (
e: Model R
e
:
Model: (R : Type ?u.4611) → [inst : IntegralDomain R] → Type ?u.4611
Model
R: Type u
R
) (
h1: SurjVal.v evr.valtn e.a1 ofN 1
h1
: evr.
valtn: {R : Type ?u.4616} → {p : R} → [inst : IntegralDomain R] → EnatValRing pSurjVal p
valtn
.
v: {R : Type ?u.4623} → {p : R} → [inst : IntegralDomain R] → SurjVal pRℕ∪∞
v
e: Model R
e
.
a1: {R : Type ?u.4630} → [inst : IntegralDomain R] → Model RR
a1
ofN: ℕ∪∞
ofN
1: ?m.4636
1
) (
h2: SurjVal.v evr.valtn e.a2 ofN 2
h2
: evr.
valtn: {R : Type ?u.4654} → {p : R} → [inst : IntegralDomain R] → EnatValRing pSurjVal p
valtn
.
v: {R : Type ?u.4658} → {p : R} → [inst : IntegralDomain R] → SurjVal pRℕ∪∞
v
e: Model R
e
.
a2: {R : Type ?u.4662} → [inst : IntegralDomain R] → Model RR
a2
ofN: ℕ∪∞
ofN
2: ?m.4666
2
) (
h3: SurjVal.v evr.valtn e.a3 ofN 3
h3
: evr.
valtn: {R : Type ?u.4676} → {p : R} → [inst : IntegralDomain R] → EnatValRing pSurjVal p
valtn
.
v: {R : Type ?u.4680} → {p : R} → [inst : IntegralDomain R] → SurjVal pRℕ∪∞
v
e: Model R
e
.
a3: {R : Type ?u.4684} → [inst : IntegralDomain R] → Model RR
a3
ofN: ℕ∪∞
ofN
3: ?m.4688
3
) (
h4: SurjVal.v evr.valtn e.a4 ofN 4
h4
: evr.
valtn: {R : Type ?u.4698} → {p : R} → [inst : IntegralDomain R] → EnatValRing pSurjVal p
valtn
.
v: {R : Type ?u.4702} → {p : R} → [inst : IntegralDomain R] → SurjVal pRℕ∪∞
v
e: Model R
e
.
a4: {R : Type ?u.4706} → [inst : IntegralDomain R] → Model RR
a4
ofN: ℕ∪∞
ofN
4: ?m.4710
4
) (
h6: SurjVal.v evr.valtn e.a6 ofN 6
h6
: evr.
valtn: {R : Type ?u.4720} → {p : R} → [inst : IntegralDomain R] → EnatValRing pSurjVal p
valtn
.
v: {R : Type ?u.4724} → {p : R} → [inst : IntegralDomain R] → SurjVal pRℕ∪∞
v
e: Model R
e
.
a6: {R : Type ?u.4728} → [inst : IntegralDomain R] → Model RR
a6
ofN: ℕ∪∞
ofN
6: ?m.4732
6
) : evr.
sub_val: {R : Type ?u.4742} → [inst : IntegralDomain R] → {p : R} → EnatValRing pRR
sub_val
e: Model R
e
.
b8: {R : Type ?u.4752} → [inst : IntegralDomain R] → Model RR
b8
8: ?m.4759
8
= evr.
sub_val: {R : Type ?u.4782} → [inst : IntegralDomain R] → {p : R} → EnatValRing pRR
sub_val
e: Model R
e
.
a1: {R : Type ?u.4792} → [inst : IntegralDomain R] → Model RR
a1
1: ?m.4796
1
* evr.
sub_val: {R : Type ?u.4798} → [inst : IntegralDomain R] → {p : R} → EnatValRing pRR
sub_val
e: Model R
e
.
a1: {R : Type ?u.4808} → [inst : IntegralDomain R] → Model RR
a1
1: ?m.4812
1
* evr.
sub_val: {R : Type ?u.4814} → [inst : IntegralDomain R] → {p : R} → EnatValRing pRR
sub_val
e: Model R
e
.
a6: {R : Type ?u.4824} → [inst : IntegralDomain R] → Model RR
a6
6: ?m.4828
6
- evr.
sub_val: {R : Type ?u.4836} → [inst : IntegralDomain R] → {p : R} → EnatValRing pRR
sub_val
e: Model R
e
.
a1: {R : Type ?u.4846} → [inst : IntegralDomain R] → Model RR
a1
1: ?m.4850
1
* evr.
sub_val: {R : Type ?u.4852} → [inst : IntegralDomain R] → {p : R} → EnatValRing pRR
sub_val
e: Model R
e
.
a3: {R : Type ?u.4862} → [inst : IntegralDomain R] → Model RR
a3
3: ?m.4866
3
* evr.
sub_val: {R : Type ?u.4868} → [inst : IntegralDomain R] → {p : R} → EnatValRing pRR
sub_val
e: Model R
e
.
a4: {R : Type ?u.4878} → [inst : IntegralDomain R] → Model RR
a4
4: ?m.4882
4
+
4: ?m.4891
4
* evr.
sub_val: {R : Type ?u.4900} → [inst : IntegralDomain R] → {p : R} → EnatValRing pRR
sub_val
e: Model R
e
.
a2: {R : Type ?u.4910} → [inst : IntegralDomain R] → Model RR
a2
2: ?m.4914
2
* evr.
sub_val: {R : Type ?u.4916} → [inst : IntegralDomain R] → {p : R} → EnatValRing pRR
sub_val
e: Model R
e
.
a6: {R : Type ?u.4926} → [inst : IntegralDomain R] → Model RR
a6
6: ?m.4930
6
+ evr.
sub_val: {R : Type ?u.4938} → [inst : IntegralDomain R] → {p : R} → EnatValRing pRR
sub_val
e: Model R
e
.
a2: {R : Type ?u.4948} → [inst : IntegralDomain R] → Model RR
a2
2: ?m.4952
2
* evr.
sub_val: {R : Type ?u.4954} → [inst : IntegralDomain R] → {p : R} → EnatValRing pRR
sub_val
e: Model R
e
.
a3: {R : Type ?u.4964} → [inst : IntegralDomain R] → Model RR
a3
3: ?m.4968
3
* evr.
sub_val: {R : Type ?u.4970} → [inst : IntegralDomain R] → {p : R} → EnatValRing pRR
sub_val
e: Model R
e
.
a3: {R : Type ?u.4980} → [inst : IntegralDomain R] → Model RR
a3
3: ?m.4984
3
- evr.
sub_val: {R : Type ?u.4989} → [inst : IntegralDomain R] → {p : R} → EnatValRing pRR
sub_val
e: Model R
e
.
a4: {R : Type ?u.4999} → [inst : IntegralDomain R] → Model RR
a4
4: ?m.5003
4
* evr.
sub_val: {R : Type ?u.5005} → [inst : IntegralDomain R] → {p : R} → EnatValRing pRR
sub_val
e: Model R
e
.
a4: {R : Type ?u.5015} → [inst : IntegralDomain R] → Model RR
a4
4: ?m.5019
4
:=
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (e.a1 * e.a1) (1 + 1) * EnatValRing.sub_val evr e.a6 6 - EnatValRing.sub_val evr e.a1 1 * EnatValRing.sub_val evr e.a3 3 * EnatValRing.sub_val evr e.a4 4 + 4 * EnatValRing.sub_val evr e.a2 2 * EnatValRing.sub_val evr e.a6 6 + EnatValRing.sub_val evr e.a2 2 * EnatValRing.sub_val evr e.a3 3 * EnatValRing.sub_val evr e.a3 3 - EnatValRing.sub_val evr e.a4 4 * EnatValRing.sub_val evr e.a4 4
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (EnatValRing.sub_val evr (e.a1 * e.a1) (1 + 1) * e.a6) 6 - EnatValRing.sub_val evr e.a1 1 * EnatValRing.sub_val evr e.a3 3 * EnatValRing.sub_val evr e.a4 4 + 4 * EnatValRing.sub_val evr e.a2 2 * EnatValRing.sub_val evr e.a6 6 + EnatValRing.sub_val evr e.a2 2 * EnatValRing.sub_val evr e.a3 3 * EnatValRing.sub_val evr e.a3 3 - EnatValRing.sub_val evr e.a4 4 * EnatValRing.sub_val evr e.a4 4
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (EnatValRing.sub_val evr (e.a1 * e.a1 * e.a6) (1 + 1)) 6 - EnatValRing.sub_val evr e.a1 1 * EnatValRing.sub_val evr e.a3 3 * EnatValRing.sub_val evr e.a4 4 + 4 * EnatValRing.sub_val evr e.a2 2 * EnatValRing.sub_val evr e.a6 6 + EnatValRing.sub_val evr e.a2 2 * EnatValRing.sub_val evr e.a3 3 * EnatValRing.sub_val evr e.a3 3 - EnatValRing.sub_val evr e.a4 4 * EnatValRing.sub_val evr e.a4 4
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (e.a1 * e.a1 * e.a6) (1 + 1 + 6) - EnatValRing.sub_val evr e.a1 1 * EnatValRing.sub_val evr e.a3 3 * EnatValRing.sub_val evr e.a4 4 + 4 * EnatValRing.sub_val evr e.a2 2 * EnatValRing.sub_val evr e.a6 6 + EnatValRing.sub_val evr e.a2 2 * EnatValRing.sub_val evr e.a3 3 * EnatValRing.sub_val evr e.a3 3 - EnatValRing.sub_val evr e.a4 4 * EnatValRing.sub_val evr e.a4 4
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (e.a1 * e.a1 * e.a6) (1 + 1 + 6) - EnatValRing.sub_val evr e.a1 1 * EnatValRing.sub_val evr e.a3 3 * EnatValRing.sub_val evr e.a4 4 + 4 * EnatValRing.sub_val evr e.a2 2 * EnatValRing.sub_val evr e.a6 6 + EnatValRing.sub_val evr e.a2 2 * EnatValRing.sub_val evr e.a3 3 * EnatValRing.sub_val evr e.a3 3 - EnatValRing.sub_val evr e.a4 4 * EnatValRing.sub_val evr e.a4 4
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (e.a1 * e.a1 * e.a6) (1 + 1 + 6) - EnatValRing.sub_val evr e.a1 1 * EnatValRing.sub_val evr e.a3 3 * EnatValRing.sub_val evr e.a4 4 + 4 * EnatValRing.sub_val evr e.a2 2 * EnatValRing.sub_val evr e.a6 6 + EnatValRing.sub_val evr e.a2 2 * EnatValRing.sub_val evr e.a3 3 * EnatValRing.sub_val evr e.a3 3 - EnatValRing.sub_val evr e.a4 4 * EnatValRing.sub_val evr e.a4 4
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (e.a1 * e.a1 * e.a6) (1 + 1 + 6) - EnatValRing.sub_val evr (EnatValRing.sub_val evr e.a1 1 * e.a3) 3 * EnatValRing.sub_val evr e.a4 4 + 4 * EnatValRing.sub_val evr e.a2 2 * EnatValRing.sub_val evr e.a6 6 + EnatValRing.sub_val evr e.a2 2 * EnatValRing.sub_val evr e.a3 3 * EnatValRing.sub_val evr e.a3 3 - EnatValRing.sub_val evr e.a4 4 * EnatValRing.sub_val evr e.a4 4
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (e.a1 * e.a1 * e.a6) (1 + 1 + 6) - EnatValRing.sub_val evr e.a1 1 * EnatValRing.sub_val evr e.a3 3 * EnatValRing.sub_val evr e.a4 4 + 4 * EnatValRing.sub_val evr e.a2 2 * EnatValRing.sub_val evr e.a6 6 + EnatValRing.sub_val evr e.a2 2 * EnatValRing.sub_val evr e.a3 3 * EnatValRing.sub_val evr e.a3 3 - EnatValRing.sub_val evr e.a4 4 * EnatValRing.sub_val evr e.a4 4
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (e.a1 * e.a1 * e.a6) (1 + 1 + 6) - EnatValRing.sub_val evr (EnatValRing.sub_val evr (e.a1 * e.a3) 1) 3 * EnatValRing.sub_val evr e.a4 4 + 4 * EnatValRing.sub_val evr e.a2 2 * EnatValRing.sub_val evr e.a6 6 + EnatValRing.sub_val evr e.a2 2 * EnatValRing.sub_val evr e.a3 3 * EnatValRing.sub_val evr e.a3 3 - EnatValRing.sub_val evr e.a4 4 * EnatValRing.sub_val evr e.a4 4
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (e.a1 * e.a1 * e.a6) (1 + 1 + 6) - EnatValRing.sub_val evr e.a1 1 * EnatValRing.sub_val evr e.a3 3 * EnatValRing.sub_val evr e.a4 4 + 4 * EnatValRing.sub_val evr e.a2 2 * EnatValRing.sub_val evr e.a6 6 + EnatValRing.sub_val evr e.a2 2 * EnatValRing.sub_val evr e.a3 3 * EnatValRing.sub_val evr e.a3 3 - EnatValRing.sub_val evr e.a4 4 * EnatValRing.sub_val evr e.a4 4
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (e.a1 * e.a1 * e.a6) (1 + 1 + 6) - EnatValRing.sub_val evr (e.a1 * e.a3) (1 + 3) * EnatValRing.sub_val evr e.a4 4 + 4 * EnatValRing.sub_val evr e.a2 2 * EnatValRing.sub_val evr e.a6 6 + EnatValRing.sub_val evr e.a2 2 * EnatValRing.sub_val evr e.a3 3 * EnatValRing.sub_val evr e.a3 3 - EnatValRing.sub_val evr e.a4 4 * EnatValRing.sub_val evr e.a4 4
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (e.a1 * e.a1 * e.a6) (1 + 1 + 6) - EnatValRing.sub_val evr e.a1 1 * EnatValRing.sub_val evr e.a3 3 * EnatValRing.sub_val evr e.a4 4 + 4 * EnatValRing.sub_val evr e.a2 2 * EnatValRing.sub_val evr e.a6 6 + EnatValRing.sub_val evr e.a2 2 * EnatValRing.sub_val evr e.a3 3 * EnatValRing.sub_val evr e.a3 3 - EnatValRing.sub_val evr e.a4 4 * EnatValRing.sub_val evr e.a4 4
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (e.a1 * e.a1 * e.a6) (1 + 1 + 6) - EnatValRing.sub_val evr (EnatValRing.sub_val evr (e.a1 * e.a3) (1 + 3) * e.a4) 4 + 4 * EnatValRing.sub_val evr e.a2 2 * EnatValRing.sub_val evr e.a6 6 + EnatValRing.sub_val evr e.a2 2 * EnatValRing.sub_val evr e.a3 3 * EnatValRing.sub_val evr e.a3 3 - EnatValRing.sub_val evr e.a4 4 * EnatValRing.sub_val evr e.a4 4
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (e.a1 * e.a1 * e.a6) (1 + 1 + 6) - EnatValRing.sub_val evr e.a1 1 * EnatValRing.sub_val evr e.a3 3 * EnatValRing.sub_val evr e.a4 4 + 4 * EnatValRing.sub_val evr e.a2 2 * EnatValRing.sub_val evr e.a6 6 + EnatValRing.sub_val evr e.a2 2 * EnatValRing.sub_val evr e.a3 3 * EnatValRing.sub_val evr e.a3 3 - EnatValRing.sub_val evr e.a4 4 * EnatValRing.sub_val evr e.a4 4
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (e.a1 * e.a1 * e.a6) (1 + 1 + 6) - EnatValRing.sub_val evr (EnatValRing.sub_val evr (e.a1 * e.a3 * e.a4) (1 + 3)) 4 + 4 * EnatValRing.sub_val evr e.a2 2 * EnatValRing.sub_val evr e.a6 6 + EnatValRing.sub_val evr e.a2 2 * EnatValRing.sub_val evr e.a3 3 * EnatValRing.sub_val evr e.a3 3 - EnatValRing.sub_val evr e.a4 4 * EnatValRing.sub_val evr e.a4 4
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (e.a1 * e.a1 * e.a6) (1 + 1 + 6) - EnatValRing.sub_val evr e.a1 1 * EnatValRing.sub_val evr e.a3 3 * EnatValRing.sub_val evr e.a4 4 + 4 * EnatValRing.sub_val evr e.a2 2 * EnatValRing.sub_val evr e.a6 6 + EnatValRing.sub_val evr e.a2 2 * EnatValRing.sub_val evr e.a3 3 * EnatValRing.sub_val evr e.a3 3 - EnatValRing.sub_val evr e.a4 4 * EnatValRing.sub_val evr e.a4 4
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (e.a1 * e.a1 * e.a6) (1 + 1 + 6) - EnatValRing.sub_val evr (e.a1 * e.a3 * e.a4) (1 + 3 + 4) + 4 * EnatValRing.sub_val evr e.a2 2 * EnatValRing.sub_val evr e.a6 6 + EnatValRing.sub_val evr e.a2 2 * EnatValRing.sub_val evr e.a3 3 * EnatValRing.sub_val evr e.a3 3 - EnatValRing.sub_val evr e.a4 4 * EnatValRing.sub_val evr e.a4 4
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (e.a1 * e.a1 * e.a6) (1 + 1 + 6) - EnatValRing.sub_val evr (e.a1 * e.a3 * e.a4) (1 + 3 + 4) + 4 * EnatValRing.sub_val evr e.a2 2 * EnatValRing.sub_val evr e.a6 6 + EnatValRing.sub_val evr e.a2 2 * EnatValRing.sub_val evr e.a3 3 * EnatValRing.sub_val evr e.a3 3 - EnatValRing.sub_val evr e.a4 4 * EnatValRing.sub_val evr e.a4 4
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (e.a1 * e.a1 * e.a6) (1 + 1 + 6) - EnatValRing.sub_val evr (e.a1 * e.a3 * e.a4) (1 + 3 + 4) + 4 * EnatValRing.sub_val evr e.a2 2 * EnatValRing.sub_val evr e.a6 6 + EnatValRing.sub_val evr e.a2 2 * EnatValRing.sub_val evr e.a3 3 * EnatValRing.sub_val evr e.a3 3 - EnatValRing.sub_val evr e.a4 4 * EnatValRing.sub_val evr e.a4 4
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (e.a1 * e.a1 * e.a6) (1 + 1 + 6) - EnatValRing.sub_val evr (e.a1 * e.a3 * e.a4) (1 + 3 + 4) + EnatValRing.sub_val evr (4 * e.a2) 2 * EnatValRing.sub_val evr e.a6 6 + EnatValRing.sub_val evr e.a2 2 * EnatValRing.sub_val evr e.a3 3 * EnatValRing.sub_val evr e.a3 3 - EnatValRing.sub_val evr e.a4 4 * EnatValRing.sub_val evr e.a4 4
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (e.a1 * e.a1 * e.a6) (1 + 1 + 6) - EnatValRing.sub_val evr (e.a1 * e.a3 * e.a4) (1 + 3 + 4) + 4 * EnatValRing.sub_val evr e.a2 2 * EnatValRing.sub_val evr e.a6 6 + EnatValRing.sub_val evr e.a2 2 * EnatValRing.sub_val evr e.a3 3 * EnatValRing.sub_val evr e.a3 3 - EnatValRing.sub_val evr e.a4 4 * EnatValRing.sub_val evr e.a4 4
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (e.a1 * e.a1 * e.a6) (1 + 1 + 6) - EnatValRing.sub_val evr (e.a1 * e.a3 * e.a4) (1 + 3 + 4) + EnatValRing.sub_val evr (EnatValRing.sub_val evr (4 * e.a2) 2 * e.a6) 6 + EnatValRing.sub_val evr e.a2 2 * EnatValRing.sub_val evr e.a3 3 * EnatValRing.sub_val evr e.a3 3 - EnatValRing.sub_val evr e.a4 4 * EnatValRing.sub_val evr e.a4 4
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (e.a1 * e.a1 * e.a6) (1 + 1 + 6) - EnatValRing.sub_val evr (e.a1 * e.a3 * e.a4) (1 + 3 + 4) + 4 * EnatValRing.sub_val evr e.a2 2 * EnatValRing.sub_val evr e.a6 6 + EnatValRing.sub_val evr e.a2 2 * EnatValRing.sub_val evr e.a3 3 * EnatValRing.sub_val evr e.a3 3 - EnatValRing.sub_val evr e.a4 4 * EnatValRing.sub_val evr e.a4 4
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (e.a1 * e.a1 * e.a6) (1 + 1 + 6) - EnatValRing.sub_val evr (e.a1 * e.a3 * e.a4) (1 + 3 + 4) + EnatValRing.sub_val evr (EnatValRing.sub_val evr (4 * e.a2 * e.a6) 2) 6 + EnatValRing.sub_val evr e.a2 2 * EnatValRing.sub_val evr e.a3 3 * EnatValRing.sub_val evr e.a3 3 - EnatValRing.sub_val evr e.a4 4 * EnatValRing.sub_val evr e.a4 4
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (e.a1 * e.a1 * e.a6) (1 + 1 + 6) - EnatValRing.sub_val evr (e.a1 * e.a3 * e.a4) (1 + 3 + 4) + 4 * EnatValRing.sub_val evr e.a2 2 * EnatValRing.sub_val evr e.a6 6 + EnatValRing.sub_val evr e.a2 2 * EnatValRing.sub_val evr e.a3 3 * EnatValRing.sub_val evr e.a3 3 - EnatValRing.sub_val evr e.a4 4 * EnatValRing.sub_val evr e.a4 4
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (e.a1 * e.a1 * e.a6) (1 + 1 + 6) - EnatValRing.sub_val evr (e.a1 * e.a3 * e.a4) (1 + 3 + 4) + EnatValRing.sub_val evr (4 * e.a2 * e.a6) (2 + 6) + EnatValRing.sub_val evr e.a2 2 * EnatValRing.sub_val evr e.a3 3 * EnatValRing.sub_val evr e.a3 3 - EnatValRing.sub_val evr e.a4 4 * EnatValRing.sub_val evr e.a4 4
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (e.a1 * e.a1 * e.a6) (1 + 1 + 6) - EnatValRing.sub_val evr (e.a1 * e.a3 * e.a4) (1 + 3 + 4) + EnatValRing.sub_val evr (4 * e.a2 * e.a6) (2 + 6) + EnatValRing.sub_val evr e.a2 2 * EnatValRing.sub_val evr e.a3 3 * EnatValRing.sub_val evr e.a3 3 - EnatValRing.sub_val evr e.a4 4 * EnatValRing.sub_val evr e.a4 4
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (e.a1 * e.a1 * e.a6) (1 + 1 + 6) - EnatValRing.sub_val evr (e.a1 * e.a3 * e.a4) (1 + 3 + 4) + EnatValRing.sub_val evr (4 * e.a2 * e.a6) (2 + 6) + EnatValRing.sub_val evr e.a2 2 * EnatValRing.sub_val evr e.a3 3 * EnatValRing.sub_val evr e.a3 3 - EnatValRing.sub_val evr e.a4 4 * EnatValRing.sub_val evr e.a4 4
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (e.a1 * e.a1 * e.a6) (1 + 1 + 6) - EnatValRing.sub_val evr (e.a1 * e.a3 * e.a4) (1 + 3 + 4) + EnatValRing.sub_val evr (4 * e.a2 * e.a6) (2 + 6) + EnatValRing.sub_val evr (e.a2 * EnatValRing.sub_val evr e.a3 3) 2 * EnatValRing.sub_val evr e.a3 3 - EnatValRing.sub_val evr e.a4 4 * EnatValRing.sub_val evr e.a4 4
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (e.a1 * e.a1 * e.a6) (1 + 1 + 6) - EnatValRing.sub_val evr (e.a1 * e.a3 * e.a4) (1 + 3 + 4) + EnatValRing.sub_val evr (4 * e.a2 * e.a6) (2 + 6) + EnatValRing.sub_val evr e.a2 2 * EnatValRing.sub_val evr e.a3 3 * EnatValRing.sub_val evr e.a3 3 - EnatValRing.sub_val evr e.a4 4 * EnatValRing.sub_val evr e.a4 4
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (e.a1 * e.a1 * e.a6) (1 + 1 + 6) - EnatValRing.sub_val evr (e.a1 * e.a3 * e.a4) (1 + 3 + 4) + EnatValRing.sub_val evr (4 * e.a2 * e.a6) (2 + 6) + EnatValRing.sub_val evr (EnatValRing.sub_val evr (e.a2 * EnatValRing.sub_val evr e.a3 3) 2 * e.a3) 3 - EnatValRing.sub_val evr e.a4 4 * EnatValRing.sub_val evr e.a4 4
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (e.a1 * e.a1 * e.a6) (1 + 1 + 6) - EnatValRing.sub_val evr (e.a1 * e.a3 * e.a4) (1 + 3 + 4) + EnatValRing.sub_val evr (4 * e.a2 * e.a6) (2 + 6) + EnatValRing.sub_val evr e.a2 2 * EnatValRing.sub_val evr e.a3 3 * EnatValRing.sub_val evr e.a3 3 - EnatValRing.sub_val evr e.a4 4 * EnatValRing.sub_val evr e.a4 4
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (e.a1 * e.a1 * e.a6) (1 + 1 + 6) - EnatValRing.sub_val evr (e.a1 * e.a3 * e.a4) (1 + 3 + 4) + EnatValRing.sub_val evr (4 * e.a2 * e.a6) (2 + 6) + EnatValRing.sub_val evr (EnatValRing.sub_val evr (EnatValRing.sub_val evr (e.a2 * e.a3) 3) 2 * e.a3) 3 - EnatValRing.sub_val evr e.a4 4 * EnatValRing.sub_val evr e.a4 4
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (e.a1 * e.a1 * e.a6) (1 + 1 + 6) - EnatValRing.sub_val evr (e.a1 * e.a3 * e.a4) (1 + 3 + 4) + EnatValRing.sub_val evr (4 * e.a2 * e.a6) (2 + 6) + EnatValRing.sub_val evr e.a2 2 * EnatValRing.sub_val evr e.a3 3 * EnatValRing.sub_val evr e.a3 3 - EnatValRing.sub_val evr e.a4 4 * EnatValRing.sub_val evr e.a4 4
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (e.a1 * e.a1 * e.a6) (1 + 1 + 6) - EnatValRing.sub_val evr (e.a1 * e.a3 * e.a4) (1 + 3 + 4) + EnatValRing.sub_val evr (4 * e.a2 * e.a6) (2 + 6) + EnatValRing.sub_val evr (EnatValRing.sub_val evr (e.a2 * e.a3) (3 + 2) * e.a3) 3 - EnatValRing.sub_val evr e.a4 4 * EnatValRing.sub_val evr e.a4 4
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (e.a1 * e.a1 * e.a6) (1 + 1 + 6) - EnatValRing.sub_val evr (e.a1 * e.a3 * e.a4) (1 + 3 + 4) + EnatValRing.sub_val evr (4 * e.a2 * e.a6) (2 + 6) + EnatValRing.sub_val evr e.a2 2 * EnatValRing.sub_val evr e.a3 3 * EnatValRing.sub_val evr e.a3 3 - EnatValRing.sub_val evr e.a4 4 * EnatValRing.sub_val evr e.a4 4
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (e.a1 * e.a1 * e.a6) (1 + 1 + 6) - EnatValRing.sub_val evr (e.a1 * e.a3 * e.a4) (1 + 3 + 4) + EnatValRing.sub_val evr (4 * e.a2 * e.a6) (2 + 6) + EnatValRing.sub_val evr (EnatValRing.sub_val evr (e.a2 * e.a3 * e.a3) (2 + 3)) 3 - EnatValRing.sub_val evr e.a4 4 * EnatValRing.sub_val evr e.a4 4
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (e.a1 * e.a1 * e.a6) (1 + 1 + 6) - EnatValRing.sub_val evr (e.a1 * e.a3 * e.a4) (1 + 3 + 4) + EnatValRing.sub_val evr (4 * e.a2 * e.a6) (2 + 6) + EnatValRing.sub_val evr e.a2 2 * EnatValRing.sub_val evr e.a3 3 * EnatValRing.sub_val evr e.a3 3 - EnatValRing.sub_val evr e.a4 4 * EnatValRing.sub_val evr e.a4 4
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (e.a1 * e.a1 * e.a6) (1 + 1 + 6) - EnatValRing.sub_val evr (e.a1 * e.a3 * e.a4) (1 + 3 + 4) + EnatValRing.sub_val evr (4 * e.a2 * e.a6) (2 + 6) + EnatValRing.sub_val evr (e.a2 * e.a3 * e.a3) (2 + 3 + 3) - EnatValRing.sub_val evr e.a4 4 * EnatValRing.sub_val evr e.a4 4
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (e.a1 * e.a1 * e.a6) (1 + 1 + 6) - EnatValRing.sub_val evr (e.a1 * e.a3 * e.a4) (1 + 3 + 4) + EnatValRing.sub_val evr (4 * e.a2 * e.a6) (2 + 6) + EnatValRing.sub_val evr (e.a2 * e.a3 * e.a3) (2 + 3 + 3) - EnatValRing.sub_val evr e.a4 4 * EnatValRing.sub_val evr e.a4 4
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (e.a1 * e.a1 * e.a6) (1 + 1 + 6) - EnatValRing.sub_val evr (e.a1 * e.a3 * e.a4) (1 + 3 + 4) + EnatValRing.sub_val evr (4 * e.a2 * e.a6) (2 + 6) + EnatValRing.sub_val evr (e.a2 * e.a3 * e.a3) (2 + 3 + 3) - EnatValRing.sub_val evr e.a4 4 * EnatValRing.sub_val evr e.a4 4
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (e.a1 * e.a1 * e.a6) (1 + 1 + 6) - EnatValRing.sub_val evr (e.a1 * e.a3 * e.a4) (1 + 3 + 4) + EnatValRing.sub_val evr (4 * e.a2 * e.a6) (2 + 6) + EnatValRing.sub_val evr (e.a2 * e.a3 * e.a3) (2 + 3 + 3) - EnatValRing.sub_val evr (EnatValRing.sub_val evr e.a4 4 * e.a4) 4
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (e.a1 * e.a1 * e.a6) (1 + 1 + 6) - EnatValRing.sub_val evr (e.a1 * e.a3 * e.a4) (1 + 3 + 4) + EnatValRing.sub_val evr (4 * e.a2 * e.a6) (2 + 6) + EnatValRing.sub_val evr (e.a2 * e.a3 * e.a3) (2 + 3 + 3) - EnatValRing.sub_val evr e.a4 4 * EnatValRing.sub_val evr e.a4 4
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (e.a1 * e.a1 * e.a6) (1 + 1 + 6) - EnatValRing.sub_val evr (e.a1 * e.a3 * e.a4) (1 + 3 + 4) + EnatValRing.sub_val evr (4 * e.a2 * e.a6) (2 + 6) + EnatValRing.sub_val evr (e.a2 * e.a3 * e.a3) (2 + 3 + 3) - EnatValRing.sub_val evr (EnatValRing.sub_val evr (e.a4 * e.a4) 4) 4
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (e.a1 * e.a1 * e.a6) (1 + 1 + 6) - EnatValRing.sub_val evr (e.a1 * e.a3 * e.a4) (1 + 3 + 4) + EnatValRing.sub_val evr (4 * e.a2 * e.a6) (2 + 6) + EnatValRing.sub_val evr (e.a2 * e.a3 * e.a3) (2 + 3 + 3) - EnatValRing.sub_val evr e.a4 4 * EnatValRing.sub_val evr e.a4 4
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (e.a1 * e.a1 * e.a6) (1 + 1 + 6) - EnatValRing.sub_val evr (e.a1 * e.a3 * e.a4) (1 + 3 + 4) + EnatValRing.sub_val evr (4 * e.a2 * e.a6) (2 + 6) + EnatValRing.sub_val evr (e.a2 * e.a3 * e.a3) (2 + 3 + 3) - EnatValRing.sub_val evr (e.a4 * e.a4) (4 + 4)
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (e.a1 * e.a1 * e.a6) (1 + 1 + 6) - EnatValRing.sub_val evr (e.a1 * e.a3 * e.a4) (1 + 3 + 4) + EnatValRing.sub_val evr (4 * e.a2 * e.a6) (2 + 6) + EnatValRing.sub_val evr (e.a2 * e.a3 * e.a3) (2 + 3 + 3) - EnatValRing.sub_val evr (e.a4 * e.a4) (4 + 4)
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

h116: SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6) ofN 1 + ofN 1 + ofN 6


EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (e.a1 * e.a1 * e.a6) (1 + 1 + 6) - EnatValRing.sub_val evr (e.a1 * e.a3 * e.a4) (1 + 3 + 4) + EnatValRing.sub_val evr (4 * e.a2 * e.a6) (2 + 6) + EnatValRing.sub_val evr (e.a2 * e.a3 * e.a3) (2 + 3 + 3) - EnatValRing.sub_val evr (e.a4 * e.a4) (4 + 4)
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

h116: SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6) ofN 1 + ofN 1 + ofN 6

h134: SurjVal.v evr.valtn (e.a1 * e.a3 * e.a4) ofN 1 + ofN 3 + ofN 4


EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (e.a1 * e.a1 * e.a6) (1 + 1 + 6) - EnatValRing.sub_val evr (e.a1 * e.a3 * e.a4) (1 + 3 + 4) + EnatValRing.sub_val evr (4 * e.a2 * e.a6) (2 + 6) + EnatValRing.sub_val evr (e.a2 * e.a3 * e.a3) (2 + 3 + 3) - EnatValRing.sub_val evr (e.a4 * e.a4) (4 + 4)
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

h116: SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6) ofN 1 + ofN 1 + ofN 6

h134: SurjVal.v evr.valtn (e.a1 * e.a3 * e.a4) ofN 1 + ofN 3 + ofN 4

h26: SurjVal.v evr.valtn (4 * e.a2 * e.a6) ofN 2 + ofN 6


EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (e.a1 * e.a1 * e.a6) (1 + 1 + 6) - EnatValRing.sub_val evr (e.a1 * e.a3 * e.a4) (1 + 3 + 4) + EnatValRing.sub_val evr (4 * e.a2 * e.a6) (2 + 6) + EnatValRing.sub_val evr (e.a2 * e.a3 * e.a3) (2 + 3 + 3) - EnatValRing.sub_val evr (e.a4 * e.a4) (4 + 4)
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

h116: SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6) ofN 1 + ofN 1 + ofN 6

h134: SurjVal.v evr.valtn (e.a1 * e.a3 * e.a4) ofN 1 + ofN 3 + ofN 4

h26: SurjVal.v evr.valtn (4 * e.a2 * e.a6) ofN 2 + ofN 6

h233: SurjVal.v evr.valtn (e.a2 * e.a3 * e.a3) ofN 2 + ofN 3 + ofN 3


EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (e.a1 * e.a1 * e.a6) (1 + 1 + 6) - EnatValRing.sub_val evr (e.a1 * e.a3 * e.a4) (1 + 3 + 4) + EnatValRing.sub_val evr (4 * e.a2 * e.a6) (2 + 6) + EnatValRing.sub_val evr (e.a2 * e.a3 * e.a3) (2 + 3 + 3) - EnatValRing.sub_val evr (e.a4 * e.a4) (4 + 4)
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

h116: SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6) ofN 1 + ofN 1 + ofN 6

h134: SurjVal.v evr.valtn (e.a1 * e.a3 * e.a4) ofN 1 + ofN 3 + ofN 4

h26: SurjVal.v evr.valtn (4 * e.a2 * e.a6) ofN 2 + ofN 6

h233: SurjVal.v evr.valtn (e.a2 * e.a3 * e.a3) ofN 2 + ofN 3 + ofN 3

h44: SurjVal.v evr.valtn (e.a4 * e.a4) ofN 4 + ofN 4


EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (e.a1 * e.a1 * e.a6) (1 + 1 + 6) - EnatValRing.sub_val evr (e.a1 * e.a3 * e.a4) (1 + 3 + 4) + EnatValRing.sub_val evr (4 * e.a2 * e.a6) (2 + 6) + EnatValRing.sub_val evr (e.a2 * e.a3 * e.a3) (2 + 3 + 3) - EnatValRing.sub_val evr (e.a4 * e.a4) (4 + 4)
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

h116: SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6) ofN (1 + 1 + 6)

h134: SurjVal.v evr.valtn (e.a1 * e.a3 * e.a4) ofN (1 + 3 + 4)

h26: SurjVal.v evr.valtn (4 * e.a2 * e.a6) ofN (2 + 6)

h233: SurjVal.v evr.valtn (e.a2 * e.a3 * e.a3) ofN (2 + 3 + 3)

h44: SurjVal.v evr.valtn (e.a4 * e.a4) ofN (4 + 4)


EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (e.a1 * e.a1 * e.a6) (1 + 1 + 6) - EnatValRing.sub_val evr (e.a1 * e.a3 * e.a4) (1 + 3 + 4) + EnatValRing.sub_val evr (4 * e.a2 * e.a6) (2 + 6) + EnatValRing.sub_val evr (e.a2 * e.a3 * e.a3) (2 + 3 + 3) - EnatValRing.sub_val evr (e.a4 * e.a4) (4 + 4)
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

h116: SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6) ofN (1 + 1 + 6)

h134: SurjVal.v evr.valtn (e.a1 * e.a3 * e.a4) ofN (1 + 3 + 4)

h26: SurjVal.v evr.valtn (4 * e.a2 * e.a6) ofN (2 + 6)

h233: SurjVal.v evr.valtn (e.a2 * e.a3 * e.a3) ofN (2 + 3 + 3)

h44: SurjVal.v evr.valtn (e.a4 * e.a4) ofN (4 + 4)


EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (e.a1 * e.a1 * e.a6) (1 + 1 + 6) - EnatValRing.sub_val evr (e.a1 * e.a3 * e.a4) (1 + 3 + 4) + EnatValRing.sub_val evr (4 * e.a2 * e.a6) (2 + 6) + EnatValRing.sub_val evr (e.a2 * e.a3 * e.a3) (2 + 3 + 3) - EnatValRing.sub_val evr (e.a4 * e.a4) (4 + 4)
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

h116: SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6) ofN (1 + 1 + 6)

h134: SurjVal.v evr.valtn (-(e.a1 * e.a3 * e.a4)) ofN (1 + 3 + 4)

h26: SurjVal.v evr.valtn (4 * e.a2 * e.a6) ofN (2 + 6)

h233: SurjVal.v evr.valtn (e.a2 * e.a3 * e.a3) ofN (2 + 3 + 3)

h44: SurjVal.v evr.valtn (e.a4 * e.a4) ofN (4 + 4)


EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (e.a1 * e.a1 * e.a6) (1 + 1 + 6) - EnatValRing.sub_val evr (e.a1 * e.a3 * e.a4) (1 + 3 + 4) + EnatValRing.sub_val evr (4 * e.a2 * e.a6) (2 + 6) + EnatValRing.sub_val evr (e.a2 * e.a3 * e.a3) (2 + 3 + 3) - EnatValRing.sub_val evr (e.a4 * e.a4) (4 + 4)
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

h116: SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6) ofN (1 + 1 + 6)

h134: SurjVal.v evr.valtn (-(e.a1 * e.a3 * e.a4)) ofN (1 + 3 + 4)

h26: SurjVal.v evr.valtn (4 * e.a2 * e.a6) ofN (2 + 6)

h233: SurjVal.v evr.valtn (e.a2 * e.a3 * e.a3) ofN (2 + 3 + 3)

h44: SurjVal.v evr.valtn (e.a4 * e.a4) ofN (4 + 4)


EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (e.a1 * e.a1 * e.a6) (1 + 1 + 6) - EnatValRing.sub_val evr (e.a1 * e.a3 * e.a4) (1 + 3 + 4) + EnatValRing.sub_val evr (4 * e.a2 * e.a6) (2 + 6) + EnatValRing.sub_val evr (e.a2 * e.a3 * e.a3) (2 + 3 + 3) - EnatValRing.sub_val evr (e.a4 * e.a4) (4 + 4)
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

h116: SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6) ofN (1 + 1 + 6)

h134: SurjVal.v evr.valtn (-(e.a1 * e.a3 * e.a4)) ofN (1 + 3 + 4)

h26: SurjVal.v evr.valtn (4 * e.a2 * e.a6) ofN (2 + 6)

h233: SurjVal.v evr.valtn (e.a2 * e.a3 * e.a3) ofN (2 + 3 + 3)

h44: SurjVal.v evr.valtn (e.a4 * e.a4) ofN (4 + 4)


EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (e.a1 * e.a1 * e.a6) (1 + 1 + 6) - EnatValRing.sub_val evr (e.a1 * e.a3 * e.a4) (1 + 3 + 4) + EnatValRing.sub_val evr (4 * e.a2 * e.a6) (2 + 6) + EnatValRing.sub_val evr (e.a2 * e.a3 * e.a3) (2 + 3 + 3) - EnatValRing.sub_val evr (e.a4 * e.a4) (4 + 4)
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

h116: SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6) ofN (1 + 1 + 6)

h134: SurjVal.v evr.valtn (-(e.a1 * e.a3 * e.a4)) ofN (1 + 3 + 4)

h26: SurjVal.v evr.valtn (4 * e.a2 * e.a6) ofN (2 + 6)

h233: SurjVal.v evr.valtn (e.a2 * e.a3 * e.a3) ofN (2 + 3 + 3)

h44: SurjVal.v evr.valtn (e.a4 * e.a4) ofN (4 + 4)


EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (e.a1 * e.a1 * e.a6) (1 + 1 + 6) - EnatValRing.sub_val evr (e.a1 * e.a3 * e.a4) (1 + 3 + 4) + EnatValRing.sub_val evr (4 * e.a2 * e.a6) (2 + 6) + EnatValRing.sub_val evr (e.a2 * e.a3 * e.a3) (2 + 3 + 3) - EnatValRing.sub_val evr (e.a4 * e.a4) (4 + 4)
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

h116: SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6) ofN (1 + 1 + 6)

h134: SurjVal.v evr.valtn (-(e.a1 * e.a3 * e.a4)) ofN (1 + 3 + 4)

h26: SurjVal.v evr.valtn (4 * e.a2 * e.a6) ofN (2 + 6)

h233: SurjVal.v evr.valtn (e.a2 * e.a3 * e.a3) ofN (2 + 3 + 3)

h44: SurjVal.v evr.valtn (-(e.a4 * e.a4)) ofN (4 + 4)


EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (e.a1 * e.a1 * e.a6) (1 + 1 + 6) - EnatValRing.sub_val evr (e.a1 * e.a3 * e.a4) (1 + 3 + 4) + EnatValRing.sub_val evr (4 * e.a2 * e.a6) (2 + 6) + EnatValRing.sub_val evr (e.a2 * e.a3 * e.a3) (2 + 3 + 3) - EnatValRing.sub_val evr (e.a4 * e.a4) (4 + 4)
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

h116: SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6) ofN (1 + 1 + 6)

h134: SurjVal.v evr.valtn (-(e.a1 * e.a3 * e.a4)) ofN (1 + 3 + 4)

h26: SurjVal.v evr.valtn (4 * e.a2 * e.a6) ofN (2 + 6)

h233: SurjVal.v evr.valtn (e.a2 * e.a3 * e.a3) ofN (2 + 3 + 3)

h44: SurjVal.v evr.valtn (-(e.a4 * e.a4)) ofN (4 + 4)


EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (e.a1 * e.a1 * e.a6) (1 + 1 + 6) - EnatValRing.sub_val evr (e.a1 * e.a3 * e.a4) (1 + 3 + 4) + EnatValRing.sub_val evr (4 * e.a2 * e.a6) (2 + 6) + EnatValRing.sub_val evr (e.a2 * e.a3 * e.a3) (2 + 3 + 3) - EnatValRing.sub_val evr (e.a4 * e.a4) (4 + 4)
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

h116: SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6) ofN (1 + 1 + 6)

h134: SurjVal.v evr.valtn (-(e.a1 * e.a3 * e.a4)) ofN (1 + 3 + 4)

h26: SurjVal.v evr.valtn (4 * e.a2 * e.a6) ofN (2 + 6)

h233: SurjVal.v evr.valtn (e.a2 * e.a3 * e.a3) ofN (2 + 3 + 3)

h44: SurjVal.v evr.valtn (-(e.a4 * e.a4)) ofN (4 + 4)


EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (e.a1 * e.a1 * e.a6) (1 + 1 + 6) - EnatValRing.sub_val evr (e.a1 * e.a3 * e.a4) (1 + 3 + 4) + EnatValRing.sub_val evr (4 * e.a2 * e.a6) (2 + 6) + EnatValRing.sub_val evr (e.a2 * e.a3 * e.a3) (2 + 3 + 3) - EnatValRing.sub_val evr (e.a4 * e.a4) (4 + 4)
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

h116: SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6) ofN (1 + 1 + 6)

h134: SurjVal.v evr.valtn (-(e.a1 * e.a3 * e.a4)) ofN (1 + 3 + 4)

h26: SurjVal.v evr.valtn (4 * e.a2 * e.a6) ofN (2 + 6)

h233: SurjVal.v evr.valtn (e.a2 * e.a3 * e.a3) ofN (2 + 3 + 3)

h44: SurjVal.v evr.valtn (-(e.a4 * e.a4)) ofN (4 + 4)


EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (e.a1 * e.a1 * e.a6) (1 + 1 + 6) - EnatValRing.sub_val evr (e.a1 * e.a3 * e.a4) (1 + 3 + 4) + EnatValRing.sub_val evr (4 * e.a2 * e.a6) (2 + 6) + EnatValRing.sub_val evr (e.a2 * e.a3 * e.a3) (2 + 3 + 3) - EnatValRing.sub_val evr (e.a4 * e.a4) (4 + 4)
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

h116: SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6) ofN (1 + 1 + 6)

h134: SurjVal.v evr.valtn (-(e.a1 * e.a3 * e.a4)) ofN (1 + 3 + 4)

h26: SurjVal.v evr.valtn (4 * e.a2 * e.a6) ofN (2 + 6)

h233: SurjVal.v evr.valtn (e.a2 * e.a3 * e.a3) ofN (2 + 3 + 3)

h44: SurjVal.v evr.valtn (-(e.a4 * e.a4)) ofN (4 + 4)


EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (e.a1 * e.a1 * e.a6) (1 + 1 + 6) - EnatValRing.sub_val evr (e.a1 * e.a3 * e.a4) (1 + 3 + 4) + EnatValRing.sub_val evr (4 * e.a2 * e.a6) (2 + 6) + EnatValRing.sub_val evr (e.a2 * e.a3 * e.a3) (2 + 3 + 3) + -EnatValRing.sub_val evr (e.a4 * e.a4) (4 + 4)
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

h116: SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6) ofN (1 + 1 + 6)

h134: SurjVal.v evr.valtn (-(e.a1 * e.a3 * e.a4)) ofN (1 + 3 + 4)

h26: SurjVal.v evr.valtn (4 * e.a2 * e.a6) ofN (2 + 6)

h233: SurjVal.v evr.valtn (e.a2 * e.a3 * e.a3) ofN (2 + 3 + 3)

h44: SurjVal.v evr.valtn (-(e.a4 * e.a4)) ofN (4 + 4)


EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (e.a1 * e.a1 * e.a6) (1 + 1 + 6) - EnatValRing.sub_val evr (e.a1 * e.a3 * e.a4) (1 + 3 + 4) + EnatValRing.sub_val evr (4 * e.a2 * e.a6) (2 + 6) + EnatValRing.sub_val evr (e.a2 * e.a3 * e.a3) (2 + 3 + 3) - EnatValRing.sub_val evr (e.a4 * e.a4) (4 + 4)
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

h116: SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6) ofN (1 + 1 + 6)

h134: SurjVal.v evr.valtn (-(e.a1 * e.a3 * e.a4)) ofN (1 + 3 + 4)

h26: SurjVal.v evr.valtn (4 * e.a2 * e.a6) ofN (2 + 6)

h233: SurjVal.v evr.valtn (e.a2 * e.a3 * e.a3) ofN (2 + 3 + 3)

h44: SurjVal.v evr.valtn (-(e.a4 * e.a4)) ofN (4 + 4)


EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (e.a1 * e.a1 * e.a6) (1 + 1 + 6) + -EnatValRing.sub_val evr (e.a1 * e.a3 * e.a4) (1 + 3 + 4) + EnatValRing.sub_val evr (4 * e.a2 * e.a6) (2 + 6) + EnatValRing.sub_val evr (e.a2 * e.a3 * e.a3) (2 + 3 + 3) + -EnatValRing.sub_val evr (e.a4 * e.a4) (4 + 4)
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

h116: SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6) ofN (1 + 1 + 6)

h134: SurjVal.v evr.valtn (-(e.a1 * e.a3 * e.a4)) ofN (1 + 3 + 4)

h26: SurjVal.v evr.valtn (4 * e.a2 * e.a6) ofN (2 + 6)

h233: SurjVal.v evr.valtn (e.a2 * e.a3 * e.a3) ofN (2 + 3 + 3)

h44: SurjVal.v evr.valtn (-(e.a4 * e.a4)) ofN (4 + 4)


EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (e.a1 * e.a1 * e.a6) (1 + 1 + 6) - EnatValRing.sub_val evr (e.a1 * e.a3 * e.a4) (1 + 3 + 4) + EnatValRing.sub_val evr (4 * e.a2 * e.a6) (2 + 6) + EnatValRing.sub_val evr (e.a2 * e.a3 * e.a3) (2 + 3 + 3) - EnatValRing.sub_val evr (e.a4 * e.a4) (4 + 4)
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

h116: SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6) ofN (1 + 1 + 6)

h134: SurjVal.v evr.valtn (-(e.a1 * e.a3 * e.a4)) ofN (1 + 3 + 4)

h26: SurjVal.v evr.valtn (4 * e.a2 * e.a6) ofN (2 + 6)

h233: SurjVal.v evr.valtn (e.a2 * e.a3 * e.a3) ofN (2 + 3 + 3)

h44: SurjVal.v evr.valtn (-(e.a4 * e.a4)) ofN (4 + 4)


EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (e.a1 * e.a1 * e.a6) (1 + 1 + 6) + EnatValRing.sub_val evr (-(e.a1 * e.a3 * e.a4)) (1 + 3 + 4) + EnatValRing.sub_val evr (4 * e.a2 * e.a6) (2 + 6) + EnatValRing.sub_val evr (e.a2 * e.a3 * e.a3) (2 + 3 + 3) + -EnatValRing.sub_val evr (e.a4 * e.a4) (4 + 4)
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

h116: SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6) ofN (1 + 1 + 6)

h134: SurjVal.v evr.valtn (-(e.a1 * e.a3 * e.a4)) ofN (1 + 3 + 4)

h26: SurjVal.v evr.valtn (4 * e.a2 * e.a6) ofN (2 + 6)

h233: SurjVal.v evr.valtn (e.a2 * e.a3 * e.a3) ofN (2 + 3 + 3)

h44: SurjVal.v evr.valtn (-(e.a4 * e.a4)) ofN (4 + 4)


EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (e.a1 * e.a1 * e.a6) (1 + 1 + 6) - EnatValRing.sub_val evr (e.a1 * e.a3 * e.a4) (1 + 3 + 4) + EnatValRing.sub_val evr (4 * e.a2 * e.a6) (2 + 6) + EnatValRing.sub_val evr (e.a2 * e.a3 * e.a3) (2 + 3 + 3) - EnatValRing.sub_val evr (e.a4 * e.a4) (4 + 4)
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

h116: SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6) ofN (1 + 1 + 6)

h134: SurjVal.v evr.valtn (-(e.a1 * e.a3 * e.a4)) ofN (1 + 3 + 4)

h26: SurjVal.v evr.valtn (4 * e.a2 * e.a6) ofN (2 + 6)

h233: SurjVal.v evr.valtn (e.a2 * e.a3 * e.a3) ofN (2 + 3 + 3)

h44: SurjVal.v evr.valtn (-(e.a4 * e.a4)) ofN (4 + 4)


EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (e.a1 * e.a1 * e.a6) (1 + 1 + 6) + EnatValRing.sub_val evr (-(e.a1 * e.a3 * e.a4)) (1 + 3 + 4) + EnatValRing.sub_val evr (4 * e.a2 * e.a6) (2 + 6) + EnatValRing.sub_val evr (e.a2 * e.a3 * e.a3) (2 + 3 + 3) + EnatValRing.sub_val evr (-(e.a4 * e.a4)) (4 + 4)
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

h116: SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6) ofN (1 + 1 + 6)

h134: SurjVal.v evr.valtn (-(e.a1 * e.a3 * e.a4)) ofN (1 + 3 + 4)

h26: SurjVal.v evr.valtn (4 * e.a2 * e.a6) ofN (2 + 6)

h233: SurjVal.v evr.valtn (e.a2 * e.a3 * e.a3) ofN (2 + 3 + 3)

h44: SurjVal.v evr.valtn (-(e.a4 * e.a4)) ofN (4 + 4)


EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (e.a1 * e.a1 * e.a6) (1 + 1 + 6) - EnatValRing.sub_val evr (e.a1 * e.a3 * e.a4) (1 + 3 + 4) + EnatValRing.sub_val evr (4 * e.a2 * e.a6) (2 + 6) + EnatValRing.sub_val evr (e.a2 * e.a3 * e.a3) (2 + 3 + 3) - EnatValRing.sub_val evr (e.a4 * e.a4) (4 + 4)
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

h116: SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6) ofN (1 + 1 + 6)

h134: SurjVal.v evr.valtn (-(e.a1 * e.a3 * e.a4)) ofN (1 + 3 + 4)

h26: SurjVal.v evr.valtn (4 * e.a2 * e.a6) ofN (2 + 6)

h233: SurjVal.v evr.valtn (e.a2 * e.a3 * e.a3) ofN (2 + 3 + 3)

h44: SurjVal.v evr.valtn (-(e.a4 * e.a4)) ofN (4 + 4)


EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (e.a1 * e.a1 * e.a6 + -(e.a1 * e.a3 * e.a4)) (1 + 1 + 6) + EnatValRing.sub_val evr (4 * e.a2 * e.a6) (2 + 6) + EnatValRing.sub_val evr (e.a2 * e.a3 * e.a3) (2 + 3 + 3) + EnatValRing.sub_val evr (-(e.a4 * e.a4)) (4 + 4)
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

h116: SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6) ofN (1 + 1 + 6)

h134: SurjVal.v evr.valtn (-(e.a1 * e.a3 * e.a4)) ofN (1 + 3 + 4)

h26: SurjVal.v evr.valtn (4 * e.a2 * e.a6) ofN (2 + 6)

h233: SurjVal.v evr.valtn (e.a2 * e.a3 * e.a3) ofN (2 + 3 + 3)

h44: SurjVal.v evr.valtn (-(e.a4 * e.a4)) ofN (4 + 4)


EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (e.a1 * e.a1 * e.a6) (1 + 1 + 6) - EnatValRing.sub_val evr (e.a1 * e.a3 * e.a4) (1 + 3 + 4) + EnatValRing.sub_val evr (4 * e.a2 * e.a6) (2 + 6) + EnatValRing.sub_val evr (e.a2 * e.a3 * e.a3) (2 + 3 + 3) - EnatValRing.sub_val evr (e.a4 * e.a4) (4 + 4)
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

h116: SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6) ofN (1 + 1 + 6)

h134: SurjVal.v evr.valtn (-(e.a1 * e.a3 * e.a4)) ofN (1 + 3 + 4)

h26: SurjVal.v evr.valtn (4 * e.a2 * e.a6) ofN (2 + 6)

h233: SurjVal.v evr.valtn (e.a2 * e.a3 * e.a3) ofN (2 + 3 + 3)

h44: SurjVal.v evr.valtn (-(e.a4 * e.a4)) ofN (4 + 4)


EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (e.a1 * e.a1 * e.a6 + -(e.a1 * e.a3 * e.a4) + 4 * e.a2 * e.a6) (2 + 6) + EnatValRing.sub_val evr (e.a2 * e.a3 * e.a3) (2 + 3 + 3) + EnatValRing.sub_val evr (-(e.a4 * e.a4)) (4 + 4)
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

h116: SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6) ofN (1 + 1 + 6)

h134: SurjVal.v evr.valtn (-(e.a1 * e.a3 * e.a4)) ofN (1 + 3 + 4)

h26: SurjVal.v evr.valtn (4 * e.a2 * e.a6) ofN (2 + 6)

h233: SurjVal.v evr.valtn (e.a2 * e.a3 * e.a3) ofN (2 + 3 + 3)

h44: SurjVal.v evr.valtn (-(e.a4 * e.a4)) ofN (4 + 4)


SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6 + -(e.a1 * e.a3 * e.a4)) ofN (2 + 6)
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

h116: SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6) ofN (1 + 1 + 6)

h134: SurjVal.v evr.valtn (-(e.a1 * e.a3 * e.a4)) ofN (1 + 3 + 4)

h26: SurjVal.v evr.valtn (4 * e.a2 * e.a6) ofN (2 + 6)

h233: SurjVal.v evr.valtn (e.a2 * e.a3 * e.a3) ofN (2 + 3 + 3)

h44: SurjVal.v evr.valtn (-(e.a4 * e.a4)) ofN (4 + 4)


EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (e.a1 * e.a1 * e.a6) (1 + 1 + 6) - EnatValRing.sub_val evr (e.a1 * e.a3 * e.a4) (1 + 3 + 4) + EnatValRing.sub_val evr (4 * e.a2 * e.a6) (2 + 6) + EnatValRing.sub_val evr (e.a2 * e.a3 * e.a3) (2 + 3 + 3) - EnatValRing.sub_val evr (e.a4 * e.a4) (4 + 4)
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

h116: SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6) ofN (1 + 1 + 6)

h134: SurjVal.v evr.valtn (-(e.a1 * e.a3 * e.a4)) ofN (1 + 3 + 4)

h26: SurjVal.v evr.valtn (4 * e.a2 * e.a6) ofN (2 + 6)

h233: SurjVal.v evr.valtn (e.a2 * e.a3 * e.a3) ofN (2 + 3 + 3)

h44: SurjVal.v evr.valtn (-(e.a4 * e.a4)) ofN (4 + 4)


EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (e.a1 * e.a1 * e.a6 + -(e.a1 * e.a3 * e.a4) + 4 * e.a2 * e.a6 + e.a2 * e.a3 * e.a3) (2 + 3 + 3) + EnatValRing.sub_val evr (-(e.a4 * e.a4)) (4 + 4)
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

h116: SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6) ofN (1 + 1 + 6)

h134: SurjVal.v evr.valtn (-(e.a1 * e.a3 * e.a4)) ofN (1 + 3 + 4)

h26: SurjVal.v evr.valtn (4 * e.a2 * e.a6) ofN (2 + 6)

h233: SurjVal.v evr.valtn (e.a2 * e.a3 * e.a3) ofN (2 + 3 + 3)

h44: SurjVal.v evr.valtn (-(e.a4 * e.a4)) ofN (4 + 4)


SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6 + -(e.a1 * e.a3 * e.a4) + 4 * e.a2 * e.a6) ofN (2 + 3 + 3)
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

h116: SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6) ofN (1 + 1 + 6)

h134: SurjVal.v evr.valtn (-(e.a1 * e.a3 * e.a4)) ofN (1 + 3 + 4)

h26: SurjVal.v evr.valtn (4 * e.a2 * e.a6) ofN (2 + 6)

h233: SurjVal.v evr.valtn (e.a2 * e.a3 * e.a3) ofN (2 + 3 + 3)

h44: SurjVal.v evr.valtn (-(e.a4 * e.a4)) ofN (4 + 4)


SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6 + -(e.a1 * e.a3 * e.a4)) ofN (2 + 6)
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

h116: SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6) ofN (1 + 1 + 6)

h134: SurjVal.v evr.valtn (-(e.a1 * e.a3 * e.a4)) ofN (1 + 3 + 4)

h26: SurjVal.v evr.valtn (4 * e.a2 * e.a6) ofN (2 + 6)

h233: SurjVal.v evr.valtn (e.a2 * e.a3 * e.a3) ofN (2 + 3 + 3)

h44: SurjVal.v evr.valtn (-(e.a4 * e.a4)) ofN (4 + 4)


EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (e.a1 * e.a1 * e.a6) (1 + 1 + 6) - EnatValRing.sub_val evr (e.a1 * e.a3 * e.a4) (1 + 3 + 4) + EnatValRing.sub_val evr (4 * e.a2 * e.a6) (2 + 6) + EnatValRing.sub_val evr (e.a2 * e.a3 * e.a3) (2 + 3 + 3) - EnatValRing.sub_val evr (e.a4 * e.a4) (4 + 4)
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

h116: SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6) ofN (1 + 1 + 6)

h134: SurjVal.v evr.valtn (-(e.a1 * e.a3 * e.a4)) ofN (1 + 3 + 4)

h26: SurjVal.v evr.valtn (4 * e.a2 * e.a6) ofN (2 + 6)

h233: SurjVal.v evr.valtn (e.a2 * e.a3 * e.a3) ofN (2 + 3 + 3)

h44: SurjVal.v evr.valtn (-(e.a4 * e.a4)) ofN (4 + 4)


EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (e.a1 * e.a1 * e.a6 + -(e.a1 * e.a3 * e.a4) + 4 * e.a2 * e.a6 + e.a2 * e.a3 * e.a3 + -(e.a4 * e.a4)) (4 + 4)
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

h116: SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6) ofN (1 + 1 + 6)

h134: SurjVal.v evr.valtn (-(e.a1 * e.a3 * e.a4)) ofN (1 + 3 + 4)

h26: SurjVal.v evr.valtn (4 * e.a2 * e.a6) ofN (2 + 6)

h233: SurjVal.v evr.valtn (e.a2 * e.a3 * e.a3) ofN (2 + 3 + 3)

h44: SurjVal.v evr.valtn (-(e.a4 * e.a4)) ofN (4 + 4)


SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6 + -(e.a1 * e.a3 * e.a4) + 4 * e.a2 * e.a6 + e.a2 * e.a3 * e.a3) ofN (4 + 4)
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

h116: SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6) ofN (1 + 1 + 6)

h134: SurjVal.v evr.valtn (-(e.a1 * e.a3 * e.a4)) ofN (1 + 3 + 4)

h26: SurjVal.v evr.valtn (4 * e.a2 * e.a6) ofN (2 + 6)

h233: SurjVal.v evr.valtn (e.a2 * e.a3 * e.a3) ofN (2 + 3 + 3)

h44: SurjVal.v evr.valtn (-(e.a4 * e.a4)) ofN (4 + 4)


SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6 + -(e.a1 * e.a3 * e.a4) + 4 * e.a2 * e.a6) ofN (2 + 3 + 3)
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

h116: SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6) ofN (1 + 1 + 6)

h134: SurjVal.v evr.valtn (-(e.a1 * e.a3 * e.a4)) ofN (1 + 3 + 4)

h26: SurjVal.v evr.valtn (4 * e.a2 * e.a6) ofN (2 + 6)

h233: SurjVal.v evr.valtn (e.a2 * e.a3 * e.a3) ofN (2 + 3 + 3)

h44: SurjVal.v evr.valtn (-(e.a4 * e.a4)) ofN (4 + 4)


SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6 + -(e.a1 * e.a3 * e.a4)) ofN (2 + 6)
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

h116: SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6) ofN (1 + 1 + 6)

h134: SurjVal.v evr.valtn (-(e.a1 * e.a3 * e.a4)) ofN (1 + 3 + 4)

h26: SurjVal.v evr.valtn (4 * e.a2 * e.a6) ofN (2 + 6)

h233: SurjVal.v evr.valtn (e.a2 * e.a3 * e.a3) ofN (2 + 3 + 3)

h44: SurjVal.v evr.valtn (-(e.a4 * e.a4)) ofN (4 + 4)


EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (e.a1 * e.a1 * e.a6) (1 + 1 + 6) - EnatValRing.sub_val evr (e.a1 * e.a3 * e.a4) (1 + 3 + 4) + EnatValRing.sub_val evr (4 * e.a2 * e.a6) (2 + 6) + EnatValRing.sub_val evr (e.a2 * e.a3 * e.a3) (2 + 3 + 3) - EnatValRing.sub_val evr (e.a4 * e.a4) (4 + 4)
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

h116: SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6) ofN (1 + 1 + 6)

h134: SurjVal.v evr.valtn (-(e.a1 * e.a3 * e.a4)) ofN (1 + 3 + 4)

h26: SurjVal.v evr.valtn (4 * e.a2 * e.a6) ofN (2 + 6)

h233: SurjVal.v evr.valtn (e.a2 * e.a3 * e.a3) ofN (2 + 3 + 3)

h44: SurjVal.v evr.valtn (-(e.a4 * e.a4)) ofN (4 + 4)


EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (e.a1 * e.a1 * e.a6 + -(e.a1 * e.a3 * e.a4) + 4 * e.a2 * e.a6 + e.a2 * e.a3 * e.a3 - e.a4 * e.a4) (4 + 4)
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

h116: SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6) ofN (1 + 1 + 6)

h134: SurjVal.v evr.valtn (-(e.a1 * e.a3 * e.a4)) ofN (1 + 3 + 4)

h26: SurjVal.v evr.valtn (4 * e.a2 * e.a6) ofN (2 + 6)

h233: SurjVal.v evr.valtn (e.a2 * e.a3 * e.a3) ofN (2 + 3 + 3)

h44: SurjVal.v evr.valtn (-(e.a4 * e.a4)) ofN (4 + 4)


SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6 + -(e.a1 * e.a3 * e.a4) + 4 * e.a2 * e.a6 + e.a2 * e.a3 * e.a3) ofN (4 + 4)
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

h116: SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6) ofN (1 + 1 + 6)

h134: SurjVal.v evr.valtn (-(e.a1 * e.a3 * e.a4)) ofN (1 + 3 + 4)

h26: SurjVal.v evr.valtn (4 * e.a2 * e.a6) ofN (2 + 6)

h233: SurjVal.v evr.valtn (e.a2 * e.a3 * e.a3) ofN (2 + 3 + 3)

h44: SurjVal.v evr.valtn (-(e.a4 * e.a4)) ofN (4 + 4)


SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6 + -(e.a1 * e.a3 * e.a4) + 4 * e.a2 * e.a6) ofN (2 + 3 + 3)
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

h116: SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6) ofN (1 + 1 + 6)

h134: SurjVal.v evr.valtn (-(e.a1 * e.a3 * e.a4)) ofN (1 + 3 + 4)

h26: SurjVal.v evr.valtn (4 * e.a2 * e.a6) ofN (2 + 6)

h233: SurjVal.v evr.valtn (e.a2 * e.a3 * e.a3) ofN (2 + 3 + 3)

h44: SurjVal.v evr.valtn (-(e.a4 * e.a4)) ofN (4 + 4)


SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6 + -(e.a1 * e.a3 * e.a4)) ofN (2 + 6)
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

h116: SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6) ofN (1 + 1 + 6)

h134: SurjVal.v evr.valtn (-(e.a1 * e.a3 * e.a4)) ofN (1 + 3 + 4)

h26: SurjVal.v evr.valtn (4 * e.a2 * e.a6) ofN (2 + 6)

h233: SurjVal.v evr.valtn (e.a2 * e.a3 * e.a3) ofN (2 + 3 + 3)

h44: SurjVal.v evr.valtn (-(e.a4 * e.a4)) ofN (4 + 4)


EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (e.a1 * e.a1 * e.a6) (1 + 1 + 6) - EnatValRing.sub_val evr (e.a1 * e.a3 * e.a4) (1 + 3 + 4) + EnatValRing.sub_val evr (4 * e.a2 * e.a6) (2 + 6) + EnatValRing.sub_val evr (e.a2 * e.a3 * e.a3) (2 + 3 + 3) - EnatValRing.sub_val evr (e.a4 * e.a4) (4 + 4)
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

h116: SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6) ofN (1 + 1 + 6)

h134: SurjVal.v evr.valtn (-(e.a1 * e.a3 * e.a4)) ofN (1 + 3 + 4)

h26: SurjVal.v evr.valtn (4 * e.a2 * e.a6) ofN (2 + 6)

h233: SurjVal.v evr.valtn (e.a2 * e.a3 * e.a3) ofN (2 + 3 + 3)

h44: SurjVal.v evr.valtn (-(e.a4 * e.a4)) ofN (4 + 4)


EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (e.a1 * e.a1 * e.a6 - e.a1 * e.a3 * e.a4 + 4 * e.a2 * e.a6 + e.a2 * e.a3 * e.a3 - e.a4 * e.a4) (4 + 4)
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

h116: SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6) ofN (1 + 1 + 6)

h134: SurjVal.v evr.valtn (-(e.a1 * e.a3 * e.a4)) ofN (1 + 3 + 4)

h26: SurjVal.v evr.valtn (4 * e.a2 * e.a6) ofN (2 + 6)

h233: SurjVal.v evr.valtn (e.a2 * e.a3 * e.a3) ofN (2 + 3 + 3)

h44: SurjVal.v evr.valtn (-(e.a4 * e.a4)) ofN (4 + 4)


SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6 + -(e.a1 * e.a3 * e.a4) + 4 * e.a2 * e.a6 + e.a2 * e.a3 * e.a3) ofN (4 + 4)
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

h116: SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6) ofN (1 + 1 + 6)

h134: SurjVal.v evr.valtn (-(e.a1 * e.a3 * e.a4)) ofN (1 + 3 + 4)

h26: SurjVal.v evr.valtn (4 * e.a2 * e.a6) ofN (2 + 6)

h233: SurjVal.v evr.valtn (e.a2 * e.a3 * e.a3) ofN (2 + 3 + 3)

h44: SurjVal.v evr.valtn (-(e.a4 * e.a4)) ofN (4 + 4)


SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6 + -(e.a1 * e.a3 * e.a4) + 4 * e.a2 * e.a6) ofN (2 + 3 + 3)
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

h116: SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6) ofN (1 + 1 + 6)

h134: SurjVal.v evr.valtn (-(e.a1 * e.a3 * e.a4)) ofN (1 + 3 + 4)

h26: SurjVal.v evr.valtn (4 * e.a2 * e.a6) ofN (2 + 6)

h233: SurjVal.v evr.valtn (e.a2 * e.a3 * e.a3) ofN (2 + 3 + 3)

h44: SurjVal.v evr.valtn (-(e.a4 * e.a4)) ofN (4 + 4)


SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6 + -(e.a1 * e.a3 * e.a4)) ofN (2 + 6)
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

h116: SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6) ofN (1 + 1 + 6)

h134: SurjVal.v evr.valtn (-(e.a1 * e.a3 * e.a4)) ofN (1 + 3 + 4)

h26: SurjVal.v evr.valtn (4 * e.a2 * e.a6) ofN (2 + 6)

h233: SurjVal.v evr.valtn (e.a2 * e.a3 * e.a3) ofN (2 + 3 + 3)

h44: SurjVal.v evr.valtn (-(e.a4 * e.a4)) ofN (4 + 4)


EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (e.a1 * e.a1 * e.a6 - e.a1 * e.a3 * e.a4 + 4 * e.a2 * e.a6 + e.a2 * e.a3 * e.a3 - e.a4 * e.a4) (4 + 4)
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

h116: SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6) ofN (1 + 1 + 6)

h134: SurjVal.v evr.valtn (-(e.a1 * e.a3 * e.a4)) ofN (1 + 3 + 4)

h26: SurjVal.v evr.valtn (4 * e.a2 * e.a6) ofN (2 + 6)

h233: SurjVal.v evr.valtn (e.a2 * e.a3 * e.a3) ofN (2 + 3 + 3)

h44: SurjVal.v evr.valtn (-(e.a4 * e.a4)) ofN (4 + 4)


SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6 + -(e.a1 * e.a3 * e.a4) + 4 * e.a2 * e.a6 + e.a2 * e.a3 * e.a3) ofN (4 + 4)
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

h116: SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6) ofN (1 + 1 + 6)

h134: SurjVal.v evr.valtn (-(e.a1 * e.a3 * e.a4)) ofN (1 + 3 + 4)

h26: SurjVal.v evr.valtn (4 * e.a2 * e.a6) ofN (2 + 6)

h233: SurjVal.v evr.valtn (e.a2 * e.a3 * e.a3) ofN (2 + 3 + 3)

h44: SurjVal.v evr.valtn (-(e.a4 * e.a4)) ofN (4 + 4)


SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6 + -(e.a1 * e.a3 * e.a4) + 4 * e.a2 * e.a6) ofN (2 + 3 + 3)
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

h116: SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6) ofN (1 + 1 + 6)

h134: SurjVal.v evr.valtn (-(e.a1 * e.a3 * e.a4)) ofN (1 + 3 + 4)

h26: SurjVal.v evr.valtn (4 * e.a2 * e.a6) ofN (2 + 6)

h233: SurjVal.v evr.valtn (e.a2 * e.a3 * e.a3) ofN (2 + 3 + 3)

h44: SurjVal.v evr.valtn (-(e.a4 * e.a4)) ofN (4 + 4)


SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6 + -(e.a1 * e.a3 * e.a4)) ofN (2 + 6)
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

h116: SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6) ofN (1 + 1 + 6)

h134: SurjVal.v evr.valtn (-(e.a1 * e.a3 * e.a4)) ofN (1 + 3 + 4)

h26: SurjVal.v evr.valtn (4 * e.a2 * e.a6) ofN (2 + 6)

h233: SurjVal.v evr.valtn (e.a2 * e.a3 * e.a3) ofN (2 + 3 + 3)

h44: SurjVal.v evr.valtn (-(e.a4 * e.a4)) ofN (4 + 4)


EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (e.a1 * e.a1 * e.a6 - e.a1 * e.a3 * e.a4 + 4 * e.a2 * e.a6 + e.a2 * e.a3 * e.a3 - e.a4 * e.a4) (4 + 4)
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

h116: SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6) ofN (1 + 1 + 6)

h134: SurjVal.v evr.valtn (-(e.a1 * e.a3 * e.a4)) ofN (1 + 3 + 4)

h26: SurjVal.v evr.valtn (4 * e.a2 * e.a6) ofN (2 + 6)

h233: SurjVal.v evr.valtn (e.a2 * e.a3 * e.a3) ofN (2 + 3 + 3)

h44: SurjVal.v evr.valtn (-(e.a4 * e.a4)) ofN (4 + 4)


EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (e.a1 * e.a1 * e.a6 - e.a1 * e.a3 * e.a4 + 4 * e.a2 * e.a6 + e.a2 * e.a3 * e.a3 - e.a4 * e.a4) (4 + 4)
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

h116: SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6) ofN (1 + 1 + 6)

h134: SurjVal.v evr.valtn (-(e.a1 * e.a3 * e.a4)) ofN (1 + 3 + 4)

h26: SurjVal.v evr.valtn (4 * e.a2 * e.a6) ofN (2 + 6)

h233: SurjVal.v evr.valtn (e.a2 * e.a3 * e.a3) ofN (2 + 3 + 3)

h44: SurjVal.v evr.valtn (-(e.a4 * e.a4)) ofN (4 + 4)


SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6 + -(e.a1 * e.a3 * e.a4) + 4 * e.a2 * e.a6 + e.a2 * e.a3 * e.a3) ofN (4 + 4)
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

h116: SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6) ofN (1 + 1 + 6)

h134: SurjVal.v evr.valtn (-(e.a1 * e.a3 * e.a4)) ofN (1 + 3 + 4)

h26: SurjVal.v evr.valtn (4 * e.a2 * e.a6) ofN (2 + 6)

h233: SurjVal.v evr.valtn (e.a2 * e.a3 * e.a3) ofN (2 + 3 + 3)

h44: SurjVal.v evr.valtn (-(e.a4 * e.a4)) ofN (4 + 4)


SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6 + -(e.a1 * e.a3 * e.a4) + 4 * e.a2 * e.a6) ofN (2 + 3 + 3)
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

h116: SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6) ofN (1 + 1 + 6)

h134: SurjVal.v evr.valtn (-(e.a1 * e.a3 * e.a4)) ofN (1 + 3 + 4)

h26: SurjVal.v evr.valtn (4 * e.a2 * e.a6) ofN (2 + 6)

h233: SurjVal.v evr.valtn (e.a2 * e.a3 * e.a3) ofN (2 + 3 + 3)

h44: SurjVal.v evr.valtn (-(e.a4 * e.a4)) ofN (4 + 4)


SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6 + -(e.a1 * e.a3 * e.a4)) ofN (2 + 6)

Goals accomplished! 🐙
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

h116: SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6) ofN (1 + 1 + 6)

h134: SurjVal.v evr.valtn (-(e.a1 * e.a3 * e.a4)) ofN (1 + 3 + 4)

h26: SurjVal.v evr.valtn (4 * e.a2 * e.a6) ofN (2 + 6)

h233: SurjVal.v evr.valtn (e.a2 * e.a3 * e.a3) ofN (2 + 3 + 3)

h44: SurjVal.v evr.valtn (-(e.a4 * e.a4)) ofN (4 + 4)


SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6 + -(e.a1 * e.a3 * e.a4) + 4 * e.a2 * e.a6 + e.a2 * e.a3 * e.a3) ofN (4 + 4)
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

h116: SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6) ofN (1 + 1 + 6)

h134: SurjVal.v evr.valtn (-(e.a1 * e.a3 * e.a4)) ofN (1 + 3 + 4)

h26: SurjVal.v evr.valtn (4 * e.a2 * e.a6) ofN (2 + 6)

h233: SurjVal.v evr.valtn (e.a2 * e.a3 * e.a3) ofN (2 + 3 + 3)

h44: SurjVal.v evr.valtn (-(e.a4 * e.a4)) ofN (4 + 4)


SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6 + -(e.a1 * e.a3 * e.a4) + 4 * e.a2 * e.a6 + e.a2 * e.a3 * e.a3) ofN (4 + 4)
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

h116: SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6) ofN (1 + 1 + 6)

h134: SurjVal.v evr.valtn (-(e.a1 * e.a3 * e.a4)) ofN (1 + 3 + 4)

h26: SurjVal.v evr.valtn (4 * e.a2 * e.a6) ofN (2 + 6)

h233: SurjVal.v evr.valtn (e.a2 * e.a3 * e.a3) ofN (2 + 3 + 3)

h44: SurjVal.v evr.valtn (-(e.a4 * e.a4)) ofN (4 + 4)


SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6 + -(e.a1 * e.a3 * e.a4) + 4 * e.a2 * e.a6) ofN (2 + 3 + 3)
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

h116: SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6) ofN (1 + 1 + 6)

h134: SurjVal.v evr.valtn (-(e.a1 * e.a3 * e.a4)) ofN (1 + 3 + 4)

h26: SurjVal.v evr.valtn (4 * e.a2 * e.a6) ofN (2 + 6)

h233: SurjVal.v evr.valtn (e.a2 * e.a3 * e.a3) ofN (2 + 3 + 3)

h44: SurjVal.v evr.valtn (-(e.a4 * e.a4)) ofN (4 + 4)


SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6 + -(e.a1 * e.a3 * e.a4)) ofN (2 + 6)

Goals accomplished! 🐙
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

h116: SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6) ofN (1 + 1 + 6)

h134: SurjVal.v evr.valtn (-(e.a1 * e.a3 * e.a4)) ofN (1 + 3 + 4)

h26: SurjVal.v evr.valtn (4 * e.a2 * e.a6) ofN (2 + 6)

h233: SurjVal.v evr.valtn (e.a2 * e.a3 * e.a3) ofN (2 + 3 + 3)

h44: SurjVal.v evr.valtn (-(e.a4 * e.a4)) ofN (4 + 4)


SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6 + -(e.a1 * e.a3 * e.a4) + 4 * e.a2 * e.a6) ofN (2 + 3 + 3)
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

h116: SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6) ofN (1 + 1 + 6)

h134: SurjVal.v evr.valtn (-(e.a1 * e.a3 * e.a4)) ofN (1 + 3 + 4)

h26: SurjVal.v evr.valtn (4 * e.a2 * e.a6) ofN (2 + 6)

h233: SurjVal.v evr.valtn (e.a2 * e.a3 * e.a3) ofN (2 + 3 + 3)

h44: SurjVal.v evr.valtn (-(e.a4 * e.a4)) ofN (4 + 4)


SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6 + -(e.a1 * e.a3 * e.a4) + 4 * e.a2 * e.a6) ofN (2 + 3 + 3)
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

h116: SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6) ofN (1 + 1 + 6)

h134: SurjVal.v evr.valtn (-(e.a1 * e.a3 * e.a4)) ofN (1 + 3 + 4)

h26: SurjVal.v evr.valtn (4 * e.a2 * e.a6) ofN (2 + 6)

h233: SurjVal.v evr.valtn (e.a2 * e.a3 * e.a3) ofN (2 + 3 + 3)

h44: SurjVal.v evr.valtn (-(e.a4 * e.a4)) ofN (4 + 4)


SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6 + -(e.a1 * e.a3 * e.a4)) ofN (2 + 6)

Goals accomplished! 🐙
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

h116: SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6) ofN (1 + 1 + 6)

h134: SurjVal.v evr.valtn (-(e.a1 * e.a3 * e.a4)) ofN (1 + 3 + 4)

h26: SurjVal.v evr.valtn (4 * e.a2 * e.a6) ofN (2 + 6)

h233: SurjVal.v evr.valtn (e.a2 * e.a3 * e.a3) ofN (2 + 3 + 3)

h44: SurjVal.v evr.valtn (-(e.a4 * e.a4)) ofN (4 + 4)


SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6 + -(e.a1 * e.a3 * e.a4)) ofN (2 + 6)
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

h116: SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6) ofN (1 + 1 + 6)

h134: SurjVal.v evr.valtn (-(e.a1 * e.a3 * e.a4)) ofN (1 + 3 + 4)

h26: SurjVal.v evr.valtn (4 * e.a2 * e.a6) ofN (2 + 6)

h233: SurjVal.v evr.valtn (e.a2 * e.a3 * e.a3) ofN (2 + 3 + 3)

h44: SurjVal.v evr.valtn (-(e.a4 * e.a4)) ofN (4 + 4)


SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6 + -(e.a1 * e.a3 * e.a4)) ofN (2 + 6)

Goals accomplished! 🐙
open EnatValRing in lemma
pi_scaling_of_discr: ∀ (evr : EnatValRing p) (e : Model R), SurjVal.v evr.valtn (b2 e) ofN 2SurjVal.v evr.valtn (b4 e) ofN 4SurjVal.v evr.valtn (b6 e) ofN 6SurjVal.v evr.valtn (b8 e) ofN 8sub_val evr (discr e) 12 = -sub_val evr (b2 e) 2 * sub_val evr (b2 e) 2 * sub_val evr (b8 e) 8 - 8 * sub_val evr (b4 e) 4 ^ 3 - 27 * sub_val evr (b6 e) 6 * sub_val evr (b6 e) 6 + 9 * sub_val evr (b2 e) 2 * sub_val evr (b4 e) 4 * sub_val evr (b6 e) 6
pi_scaling_of_discr
(evr :
EnatValRing: {R : Type ?u.7528} → R[inst : IntegralDomain R] → Type ?u.7528
EnatValRing
p: R
p
) (
e: Model R
e
:
Model: (R : Type ?u.7536) → [inst : IntegralDomain R] → Type ?u.7536
Model
R: Type u
R
) (
hb2: SurjVal.v evr.valtn (b2 e) ofN 2
hb2
: evr.
valtn: {R : Type ?u.7541} → {p : R} → [inst : IntegralDomain R] → EnatValRing pSurjVal p
valtn
.
v: {R : Type ?u.7548} → {p : R} → [inst : IntegralDomain R] → SurjVal pRℕ∪∞
v
e: Model R
e
.
b2: {R : Type ?u.7555} → [inst : IntegralDomain R] → Model RR
b2
ofN: ℕ∪∞
ofN
2: ?m.7564
2
) (
hb4: SurjVal.v evr.valtn (b4 e) ofN 4
hb4
: evr.
valtn: {R : Type ?u.7581} → {p : R} → [inst : IntegralDomain R] → EnatValRing pSurjVal p
valtn
.
v: {R : Type ?u.7585} → {p : R} → [inst : IntegralDomain R] → SurjVal pRℕ∪∞
v
e: Model R
e
.
b4: {R : Type ?u.7589} → [inst : IntegralDomain R] → Model RR
b4
ofN: ℕ∪∞
ofN
4: ?m.7596
4
) (
hb6: SurjVal.v evr.valtn (b6 e) ofN 6
hb6
: evr.
valtn: {R : Type ?u.7606} → {p : R} → [inst : IntegralDomain R] → EnatValRing pSurjVal p
valtn
.
v: {R : Type ?u.7610} → {p : R} → [inst : IntegralDomain R] → SurjVal pRℕ∪∞
v
e: Model R
e
.
b6: {R : Type ?u.7614} → [inst : IntegralDomain R] → Model RR
b6
ofN: ℕ∪∞
ofN
6: ?m.7621
6
) (
hb8: SurjVal.v evr.valtn (b8 e) ofN 8
hb8
: evr.
valtn: {R : Type ?u.7631} → {p : R} → [inst : IntegralDomain R] → EnatValRing pSurjVal p
valtn
.
v: {R : Type ?u.7635} → {p : R} → [inst : IntegralDomain R] → SurjVal pRℕ∪∞
v
e: Model R
e
.
b8: {R : Type ?u.7639} → [inst : IntegralDomain R] → Model RR
b8
ofN: ℕ∪∞
ofN
8: ?m.7646
8
) : evr.
sub_val: {R : Type ?u.7656} → [inst : IntegralDomain R] → {p : R} → EnatValRing pRR
sub_val
e: Model R
e
.
discr: {R : Type ?u.7666} → [inst : IntegralDomain R] → Model RR
discr
12: ?m.7673
12
= -evr.
sub_val: {R : Type ?u.7694} → [inst : IntegralDomain R] → {p : R} → EnatValRing pRR
sub_val
e: Model R
e
.
b2: {R : Type ?u.7704} → [inst : IntegralDomain R] → Model RR
b2
2: ?m.7711
2
* evr.
sub_val: {R : Type ?u.7713} → [inst : IntegralDomain R] → {p : R} → EnatValRing pRR
sub_val
e: Model R
e
.
b2: {R : Type ?u.7723} → [inst : IntegralDomain R] → Model RR
b2
2: ?m.7730
2
* evr.
sub_val: {R : Type ?u.7732} → [inst : IntegralDomain R] → {p : R} → EnatValRing pRR
sub_val
e: Model R
e
.
b8: {R : Type ?u.7742} → [inst : IntegralDomain R] → Model RR
b8
8: ?m.7749
8
-
8: ?m.7755
8
* ((evr.
sub_val: {R : Type ?u.7767} → [inst : IntegralDomain R] → {p : R} → EnatValRing pRR
sub_val
e: Model R
e
.
b4: {R : Type ?u.7777} → [inst : IntegralDomain R] → Model RR
b4
4: ?m.7784
4
) ^
3: ?m.7787
3
) -
27: ?m.7803
27
* evr.
sub_val: {R : Type ?u.7812} → [inst : IntegralDomain R] → {p : R} → EnatValRing pRR
sub_val
e: Model R
e
.
b6: {R : Type ?u.7822} → [inst : IntegralDomain R] → Model RR
b6
6: ?m.7829
6
* evr.
sub_val: {R : Type ?u.7831} → [inst : IntegralDomain R] → {p : R} → EnatValRing pRR
sub_val
e: Model R
e
.
b6: {R : Type ?u.7841} → [inst : IntegralDomain R] → Model RR
b6
6: ?m.7848
6
+
9: ?m.7860
9
* evr.
sub_val: {R : Type ?u.7869} → [inst : IntegralDomain R] → {p : R} → EnatValRing pRR
sub_val
e: Model R
e
.
b2: {R : Type ?u.7879} → [inst : IntegralDomain R] → Model RR
b2
2: ?m.7886
2
* evr.
sub_val: {R : Type ?u.7888} → [inst : IntegralDomain R] → {p : R} → EnatValRing pRR
sub_val
e: Model R
e
.
b4: {R : Type ?u.7898} → [inst : IntegralDomain R] → Model RR
b4
4: ?m.7905
4
* evr.
sub_val: {R : Type ?u.7907} → [inst : IntegralDomain R] → {p : R} → EnatValRing pRR
sub_val
e: Model R
e
.
b6: {R : Type ?u.7917} → [inst : IntegralDomain R] → Model RR
b6
6: ?m.7924
6
:=
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


sub_val evr (discr e) 12 = -sub_val evr (b2 e) 2 * sub_val evr (b2 e) 2 * sub_val evr (b8 e) 8 - 8 * sub_val evr (b4 e) 4 ^ 3 - 27 * sub_val evr (b6 e) 6 * sub_val evr (b6 e) 6 + 9 * sub_val evr (b2 e) 2 * sub_val evr (b4 e) 4 * sub_val evr (b6 e) 6
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


sub_val evr (discr e) 12 = -sub_val evr (b2 e) 2 * sub_val evr (b2 e) 2 * sub_val evr (b8 e) 8 - 8 * sub_val evr (b4 e) 4 ^ 3 - 27 * sub_val evr (b6 e) 6 * sub_val evr (b6 e) 6 + 9 * sub_val evr (b2 e) 2 * sub_val evr (b4 e) 4 * sub_val evr (b6 e) 6
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


sub_val evr (-b2 e * b2 e * b8 e - 8 * b4 e ^ 3 - 27 * b6 e * b6 e + 9 * b2 e * b4 e * b6 e) 12 = -sub_val evr (b2 e) 2 * sub_val evr (b2 e) 2 * sub_val evr (b8 e) 8 - 8 * sub_val evr (b4 e) 4 ^ 3 - 27 * sub_val evr (b6 e) 6 * sub_val evr (b6 e) 6 + 9 * sub_val evr (b2 e) 2 * sub_val evr (b4 e) 4 * sub_val evr (b6 e) 6
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


sub_val evr (discr e) 12 = -sub_val evr (b2 e) 2 * sub_val evr (b2 e) 2 * sub_val evr (b8 e) 8 - 8 * sub_val evr (b4 e) 4 ^ 3 - 27 * sub_val evr (b6 e) 6 * sub_val evr (b6 e) 6 + 9 * sub_val evr (b2 e) 2 * sub_val evr (b4 e) 4 * sub_val evr (b6 e) 6
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


sub_val evr (-b2 e * b2 e * b8 e - 8 * b4 e ^ 3 - 27 * b6 e * b6 e) 12 + sub_val evr (9 * b2 e * b4 e * b6 e) 12 = -sub_val evr (b2 e) 2 * sub_val evr (b2 e) 2 * sub_val evr (b8 e) 8 - 8 * sub_val evr (b4 e) 4 ^ 3 - 27 * sub_val evr (b6 e) 6 * sub_val evr (b6 e) 6 + 9 * sub_val evr (b2 e) 2 * sub_val evr (b4 e) 4 * sub_val evr (b6 e) 6
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hx
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e - 8 * b4 e ^ 3 - 27 * b6 e * b6 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hy
SurjVal.v evr.valtn (9 * b2 e * b4 e * b6 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


sub_val evr (discr e) 12 = -sub_val evr (b2 e) 2 * sub_val evr (b2 e) 2 * sub_val evr (b8 e) 8 - 8 * sub_val evr (b4 e) 4 ^ 3 - 27 * sub_val evr (b6 e) 6 * sub_val evr (b6 e) 6 + 9 * sub_val evr (b2 e) 2 * sub_val evr (b4 e) 4 * sub_val evr (b6 e) 6
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


sub_val evr (-b2 e * b2 e * b8 e - 8 * b4 e ^ 3) 12 - sub_val evr (27 * b6 e * b6 e) 12 + sub_val evr (9 * b2 e * b4 e * b6 e) 12 = -sub_val evr (b2 e) 2 * sub_val evr (b2 e) 2 * sub_val evr (b8 e) 8 - 8 * sub_val evr (b4 e) 4 ^ 3 - 27 * sub_val evr (b6 e) 6 * sub_val evr (b6 e) 6 + 9 * sub_val evr (b2 e) 2 * sub_val evr (b4 e) 4 * sub_val evr (b6 e) 6
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hx
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e - 8 * b4 e ^ 3) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hy
SurjVal.v evr.valtn (27 * b6 e * b6 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hx
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e - 8 * b4 e ^ 3 - 27 * b6 e * b6 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hy
SurjVal.v evr.valtn (9 * b2 e * b4 e * b6 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


sub_val evr (discr e) 12 = -sub_val evr (b2 e) 2 * sub_val evr (b2 e) 2 * sub_val evr (b8 e) 8 - 8 * sub_val evr (b4 e) 4 ^ 3 - 27 * sub_val evr (b6 e) 6 * sub_val evr (b6 e) 6 + 9 * sub_val evr (b2 e) 2 * sub_val evr (b4 e) 4 * sub_val evr (b6 e) 6
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


sub_val evr (-b2 e * b2 e * b8 e) 12 - sub_val evr (8 * b4 e ^ 3) 12 - sub_val evr (27 * b6 e * b6 e) 12 + sub_val evr (9 * b2 e * b4 e * b6 e) 12 = -sub_val evr (b2 e) 2 * sub_val evr (b2 e) 2 * sub_val evr (b8 e) 8 - 8 * sub_val evr (b4 e) 4 ^ 3 - 27 * sub_val evr (b6 e) 6 * sub_val evr (b6 e) 6 + 9 * sub_val evr (b2 e) 2 * sub_val evr (b4 e) 4 * sub_val evr (b6 e) 6
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hx
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hy
SurjVal.v evr.valtn (8 * b4 e ^ 3) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hx
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e - 8 * b4 e ^ 3) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hy
SurjVal.v evr.valtn (27 * b6 e * b6 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hx
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e - 8 * b4 e ^ 3 - 27 * b6 e * b6 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hy
SurjVal.v evr.valtn (9 * b2 e * b4 e * b6 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


sub_val evr (discr e) 12 = -sub_val evr (b2 e) 2 * sub_val evr (b2 e) 2 * sub_val evr (b8 e) 8 - 8 * sub_val evr (b4 e) 4 ^ 3 - 27 * sub_val evr (b6 e) 6 * sub_val evr (b6 e) 6 + 9 * sub_val evr (b2 e) 2 * sub_val evr (b4 e) 4 * sub_val evr (b6 e) 6
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


sub_val evr (-b2 e * b2 e) 4 * sub_val evr (b8 e) 8 - sub_val evr (8 * b4 e ^ 3) 12 - sub_val evr (27 * b6 e * b6 e) 12 + sub_val evr (9 * b2 e * b4 e * b6 e) 12 = -sub_val evr (b2 e) 2 * sub_val evr (b2 e) 2 * sub_val evr (b8 e) 8 - 8 * sub_val evr (b4 e) 4 ^ 3 - 27 * sub_val evr (b6 e) 6 * sub_val evr (b6 e) 6 + 9 * sub_val evr (b2 e) 2 * sub_val evr (b4 e) 4 * sub_val evr (b6 e) 6
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


4 + 8 = 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


SurjVal.v evr.valtn (-b2 e * b2 e) ofN 4
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hx
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hy
SurjVal.v evr.valtn (8 * b4 e ^ 3) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hx
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e - 8 * b4 e ^ 3) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hy
SurjVal.v evr.valtn (27 * b6 e * b6 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hx
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e - 8 * b4 e ^ 3 - 27 * b6 e * b6 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hy
SurjVal.v evr.valtn (9 * b2 e * b4 e * b6 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


sub_val evr (discr e) 12 = -sub_val evr (b2 e) 2 * sub_val evr (b2 e) 2 * sub_val evr (b8 e) 8 - 8 * sub_val evr (b4 e) 4 ^ 3 - 27 * sub_val evr (b6 e) 6 * sub_val evr (b6 e) 6 + 9 * sub_val evr (b2 e) 2 * sub_val evr (b4 e) 4 * sub_val evr (b6 e) 6
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


sub_val evr (-b2 e) 2 * sub_val evr (b2 e) 2 * sub_val evr (b8 e) 8 - sub_val evr (8 * b4 e ^ 3) 12 - sub_val evr (27 * b6 e * b6 e) 12 + sub_val evr (9 * b2 e * b4 e * b6 e) 12 = -sub_val evr (b2 e) 2 * sub_val evr (b2 e) 2 * sub_val evr (b8 e) 8 - 8 * sub_val evr (b4 e) 4 ^ 3 - 27 * sub_val evr (b6 e) 6 * sub_val evr (b6 e) 6 + 9 * sub_val evr (b2 e) 2 * sub_val evr (b4 e) 4 * sub_val evr (b6 e) 6
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


2 + 2 = 4
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


SurjVal.v evr.valtn (-b2 e) ofN 2
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


4 + 8 = 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


SurjVal.v evr.valtn (-b2 e * b2 e) ofN 4
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hx
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hy
SurjVal.v evr.valtn (8 * b4 e ^ 3) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hx
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e - 8 * b4 e ^ 3) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hy
SurjVal.v evr.valtn (27 * b6 e * b6 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hx
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e - 8 * b4 e ^ 3 - 27 * b6 e * b6 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hy
SurjVal.v evr.valtn (9 * b2 e * b4 e * b6 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


sub_val evr (discr e) 12 = -sub_val evr (b2 e) 2 * sub_val evr (b2 e) 2 * sub_val evr (b8 e) 8 - 8 * sub_val evr (b4 e) 4 ^ 3 - 27 * sub_val evr (b6 e) 6 * sub_val evr (b6 e) 6 + 9 * sub_val evr (b2 e) 2 * sub_val evr (b4 e) 4 * sub_val evr (b6 e) 6
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


sub_val evr (-b2 e) 2 * sub_val evr (b2 e) 2 * sub_val evr (b8 e) 8 - sub_val evr (8 * b4 e ^ 3) 12 - sub_val evr (27 * b6 e) 6 * sub_val evr (b6 e) 6 + sub_val evr (9 * b2 e * b4 e * b6 e) 12 = -sub_val evr (b2 e) 2 * sub_val evr (b2 e) 2 * sub_val evr (b8 e) 8 - 8 * sub_val evr (b4 e) 4 ^ 3 - 27 * sub_val evr (b6 e) 6 * sub_val evr (b6 e) 6 + 9 * sub_val evr (b2 e) 2 * sub_val evr (b4 e) 4 * sub_val evr (b6 e) 6
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


6 + 6 = 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


SurjVal.v evr.valtn (27 * b6 e) ofN 6
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


2 + 2 = 4
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


SurjVal.v evr.valtn (-b2 e) ofN 2
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


4 + 8 = 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


SurjVal.v evr.valtn (-b2 e * b2 e) ofN 4
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hx
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hy
SurjVal.v evr.valtn (8 * b4 e ^ 3) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hx
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e - 8 * b4 e ^ 3) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hy
SurjVal.v evr.valtn (27 * b6 e * b6 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hx
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e - 8 * b4 e ^ 3 - 27 * b6 e * b6 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hy
SurjVal.v evr.valtn (9 * b2 e * b4 e * b6 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


sub_val evr (discr e) 12 = -sub_val evr (b2 e) 2 * sub_val evr (b2 e) 2 * sub_val evr (b8 e) 8 - 8 * sub_val evr (b4 e) 4 ^ 3 - 27 * sub_val evr (b6 e) 6 * sub_val evr (b6 e) 6 + 9 * sub_val evr (b2 e) 2 * sub_val evr (b4 e) 4 * sub_val evr (b6 e) 6
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


sub_val evr (-b2 e) 2 * sub_val evr (b2 e) 2 * sub_val evr (b8 e) 8 - sub_val evr (8 * b4 e ^ 3) 12 - 27 * sub_val evr (b6 e) 6 * sub_val evr (b6 e) 6 + sub_val evr (9 * b2 e * b4 e * b6 e) 12 = -sub_val evr (b2 e) 2 * sub_val evr (b2 e) 2 * sub_val evr (b8 e) 8 - 8 * sub_val evr (b4 e) 4 ^ 3 - 27 * sub_val evr (b6 e) 6 * sub_val evr (b6 e) 6 + 9 * sub_val evr (b2 e) 2 * sub_val evr (b4 e) 4 * sub_val evr (b6 e) 6
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


6 + 6 = 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


SurjVal.v evr.valtn (27 * b6 e) ofN 6
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


2 + 2 = 4
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


SurjVal.v evr.valtn (-b2 e) ofN 2
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


4 + 8 = 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


SurjVal.v evr.valtn (-b2 e * b2 e) ofN 4
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hx
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hy
SurjVal.v evr.valtn (8 * b4 e ^ 3) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hx
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e - 8 * b4 e ^ 3) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hy
SurjVal.v evr.valtn (27 * b6 e * b6 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hx
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e - 8 * b4 e ^ 3 - 27 * b6 e * b6 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hy
SurjVal.v evr.valtn (9 * b2 e * b4 e * b6 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


sub_val evr (discr e) 12 = -sub_val evr (b2 e) 2 * sub_val evr (b2 e) 2 * sub_val evr (b8 e) 8 - 8 * sub_val evr (b4 e) 4 ^ 3 - 27 * sub_val evr (b6 e) 6 * sub_val evr (b6 e) 6 + 9 * sub_val evr (b2 e) 2 * sub_val evr (b4 e) 4 * sub_val evr (b6 e) 6
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


sub_val evr (-b2 e) 2 * sub_val evr (b2 e) 2 * sub_val evr (b8 e) 8 - sub_val evr (8 * b4 e ^ 3) 12 - 27 * sub_val evr (b6 e) 6 * sub_val evr (b6 e) 6 + sub_val evr (9 * b2 e * b4 e) 6 * sub_val evr (b6 e) 6 = -sub_val evr (b2 e) 2 * sub_val evr (b2 e) 2 * sub_val evr (b8 e) 8 - 8 * sub_val evr (b4 e) 4 ^ 3 - 27 * sub_val evr (b6 e) 6 * sub_val evr (b6 e) 6 + 9 * sub_val evr (b2 e) 2 * sub_val evr (b4 e) 4 * sub_val evr (b6 e) 6
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


6 + 6 = 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


SurjVal.v evr.valtn (9 * b2 e * b4 e) ofN 6
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


6 + 6 = 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


SurjVal.v evr.valtn (27 * b6 e) ofN 6
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


2 + 2 = 4
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


SurjVal.v evr.valtn (-b2 e) ofN 2
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


4 + 8 = 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


SurjVal.v evr.valtn (-b2 e * b2 e) ofN 4
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hx
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hy
SurjVal.v evr.valtn (8 * b4 e ^ 3) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hx
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e - 8 * b4 e ^ 3) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hy
SurjVal.v evr.valtn (27 * b6 e * b6 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hx
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e - 8 * b4 e ^ 3 - 27 * b6 e * b6 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hy
SurjVal.v evr.valtn (9 * b2 e * b4 e * b6 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


sub_val evr (discr e) 12 = -sub_val evr (b2 e) 2 * sub_val evr (b2 e) 2 * sub_val evr (b8 e) 8 - 8 * sub_val evr (b4 e) 4 ^ 3 - 27 * sub_val evr (b6 e) 6 * sub_val evr (b6 e) 6 + 9 * sub_val evr (b2 e) 2 * sub_val evr (b4 e) 4 * sub_val evr (b6 e) 6
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


sub_val evr (-b2 e) 2 * sub_val evr (b2 e) 2 * sub_val evr (b8 e) 8 - sub_val evr (8 * b4 e ^ 3) 12 - 27 * sub_val evr (b6 e) 6 * sub_val evr (b6 e) 6 + sub_val evr (9 * b2 e) 2 * sub_val evr (b4 e) 4 * sub_val evr (b6 e) 6 = -sub_val evr (b2 e) 2 * sub_val evr (b2 e) 2 * sub_val evr (b8 e) 8 - 8 * sub_val evr (b4 e) 4 ^ 3 - 27 * sub_val evr (b6 e) 6 * sub_val evr (b6 e) 6 + 9 * sub_val evr (b2 e) 2 * sub_val evr (b4 e) 4 * sub_val evr (b6 e) 6
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


2 + 4 = 6
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


SurjVal.v evr.valtn (9 * b2 e) ofN 2
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


6 + 6 = 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


SurjVal.v evr.valtn (9 * b2 e * b4 e) ofN 6
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


6 + 6 = 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


SurjVal.v evr.valtn (27 * b6 e) ofN 6
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


2 + 2 = 4
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


SurjVal.v evr.valtn (-b2 e) ofN 2
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


4 + 8 = 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


SurjVal.v evr.valtn (-b2 e * b2 e) ofN 4
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hx
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hy
SurjVal.v evr.valtn (8 * b4 e ^ 3) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hx
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e - 8 * b4 e ^ 3) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hy
SurjVal.v evr.valtn (27 * b6 e * b6 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hx
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e - 8 * b4 e ^ 3 - 27 * b6 e * b6 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hy
SurjVal.v evr.valtn (9 * b2 e * b4 e * b6 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


sub_val evr (discr e) 12 = -sub_val evr (b2 e) 2 * sub_val evr (b2 e) 2 * sub_val evr (b8 e) 8 - 8 * sub_val evr (b4 e) 4 ^ 3 - 27 * sub_val evr (b6 e) 6 * sub_val evr (b6 e) 6 + 9 * sub_val evr (b2 e) 2 * sub_val evr (b4 e) 4 * sub_val evr (b6 e) 6
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


sub_val evr (-b2 e) 2 * sub_val evr (b2 e) 2 * sub_val evr (b8 e) 8 - sub_val evr (8 * b4 e ^ 3) 12 - 27 * sub_val evr (b6 e) 6 * sub_val evr (b6 e) 6 + 9 * sub_val evr (b2 e) 2 * sub_val evr (b4 e) 4 * sub_val evr (b6 e) 6 = -sub_val evr (b2 e) 2 * sub_val evr (b2 e) 2 * sub_val evr (b8 e) 8 - 8 * sub_val evr (b4 e) 4 ^ 3 - 27 * sub_val evr (b6 e) 6 * sub_val evr (b6 e) 6 + 9 * sub_val evr (b2 e) 2 * sub_val evr (b4 e) 4 * sub_val evr (b6 e) 6
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


2 + 4 = 6
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


SurjVal.v evr.valtn (9 * b2 e) ofN 2
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


6 + 6 = 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


SurjVal.v evr.valtn (9 * b2 e * b4 e) ofN 6
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


6 + 6 = 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


SurjVal.v evr.valtn (27 * b6 e) ofN 6
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


2 + 2 = 4
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


SurjVal.v evr.valtn (-b2 e) ofN 2
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


4 + 8 = 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


SurjVal.v evr.valtn (-b2 e * b2 e) ofN 4
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hx
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hy
SurjVal.v evr.valtn (8 * b4 e ^ 3) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hx
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e - 8 * b4 e ^ 3) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hy
SurjVal.v evr.valtn (27 * b6 e * b6 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hx
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e - 8 * b4 e ^ 3 - 27 * b6 e * b6 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hy
SurjVal.v evr.valtn (9 * b2 e * b4 e * b6 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


sub_val evr (discr e) 12 = -sub_val evr (b2 e) 2 * sub_val evr (b2 e) 2 * sub_val evr (b8 e) 8 - 8 * sub_val evr (b4 e) 4 ^ 3 - 27 * sub_val evr (b6 e) 6 * sub_val evr (b6 e) 6 + 9 * sub_val evr (b2 e) 2 * sub_val evr (b4 e) 4 * sub_val evr (b6 e) 6
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


sub_val evr (-b2 e) 2 * sub_val evr (b2 e) 2 * sub_val evr (b8 e) 8 - 8 * sub_val evr (b4 e ^ 3) 12 - 27 * sub_val evr (b6 e) 6 * sub_val evr (b6 e) 6 + 9 * sub_val evr (b2 e) 2 * sub_val evr (b4 e) 4 * sub_val evr (b6 e) 6 = -sub_val evr (b2 e) 2 * sub_val evr (b2 e) 2 * sub_val evr (b8 e) 8 - 8 * sub_val evr (b4 e) 4 ^ 3 - 27 * sub_val evr (b6 e) 6 * sub_val evr (b6 e) 6 + 9 * sub_val evr (b2 e) 2 * sub_val evr (b4 e) 4 * sub_val evr (b6 e) 6
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hy
SurjVal.v evr.valtn (b4 e ^ 3) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


2 + 4 = 6
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


SurjVal.v evr.valtn (9 * b2 e) ofN 2
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


6 + 6 = 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


SurjVal.v evr.valtn (9 * b2 e * b4 e) ofN 6
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


6 + 6 = 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


SurjVal.v evr.valtn (27 * b6 e) ofN 6
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


2 + 2 = 4
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


SurjVal.v evr.valtn (-b2 e) ofN 2
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


4 + 8 = 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


SurjVal.v evr.valtn (-b2 e * b2 e) ofN 4
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hx
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hy
SurjVal.v evr.valtn (8 * b4 e ^ 3) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hx
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e - 8 * b4 e ^ 3) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hy
SurjVal.v evr.valtn (27 * b6 e * b6 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hx
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e - 8 * b4 e ^ 3 - 27 * b6 e * b6 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hy
SurjVal.v evr.valtn (9 * b2 e * b4 e * b6 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


sub_val evr (discr e) 12 = -sub_val evr (b2 e) 2 * sub_val evr (b2 e) 2 * sub_val evr (b8 e) 8 - 8 * sub_val evr (b4 e) 4 ^ 3 - 27 * sub_val evr (b6 e) 6 * sub_val evr (b6 e) 6 + 9 * sub_val evr (b2 e) 2 * sub_val evr (b4 e) 4 * sub_val evr (b6 e) 6
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


sub_val evr (-b2 e) 2 * sub_val evr (b2 e) 2 * sub_val evr (b8 e) 8 - 8 * sub_val evr (b4 e) 4 ^ 3 - 27 * sub_val evr (b6 e) 6 * sub_val evr (b6 e) 6 + 9 * sub_val evr (b2 e) 2 * sub_val evr (b4 e) 4 * sub_val evr (b6 e) 6 = -sub_val evr (b2 e) 2 * sub_val evr (b2 e) 2 * sub_val evr (b8 e) 8 - 8 * sub_val evr (b4 e) 4 ^ 3 - 27 * sub_val evr (b6 e) 6 * sub_val evr (b6 e) 6 + 9 * sub_val evr (b2 e) 2 * sub_val evr (b4 e) 4 * sub_val evr (b6 e) 6
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


3 * 4 = 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hy
SurjVal.v evr.valtn (b4 e ^ 3) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


2 + 4 = 6
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


SurjVal.v evr.valtn (9 * b2 e) ofN 2
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


6 + 6 = 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


SurjVal.v evr.valtn (9 * b2 e * b4 e) ofN 6
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


6 + 6 = 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


SurjVal.v evr.valtn (27 * b6 e) ofN 6
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


2 + 2 = 4
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


SurjVal.v evr.valtn (-b2 e) ofN 2
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


4 + 8 = 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


SurjVal.v evr.valtn (-b2 e * b2 e) ofN 4
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hx
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hy
SurjVal.v evr.valtn (8 * b4 e ^ 3) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hx
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e - 8 * b4 e ^ 3) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hy
SurjVal.v evr.valtn (27 * b6 e * b6 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hx
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e - 8 * b4 e ^ 3 - 27 * b6 e * b6 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hy
SurjVal.v evr.valtn (9 * b2 e * b4 e * b6 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


sub_val evr (discr e) 12 = -sub_val evr (b2 e) 2 * sub_val evr (b2 e) 2 * sub_val evr (b8 e) 8 - 8 * sub_val evr (b4 e) 4 ^ 3 - 27 * sub_val evr (b6 e) 6 * sub_val evr (b6 e) 6 + 9 * sub_val evr (b2 e) 2 * sub_val evr (b4 e) 4 * sub_val evr (b6 e) 6
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


-sub_val evr (b2 e) 2 * sub_val evr (b2 e) 2 * sub_val evr (b8 e) 8 - 8 * sub_val evr (b4 e) 4 ^ 3 - 27 * sub_val evr (b6 e) 6 * sub_val evr (b6 e) 6 + 9 * sub_val evr (b2 e) 2 * sub_val evr (b4 e) 4 * sub_val evr (b6 e) 6 = -sub_val evr (b2 e) 2 * sub_val evr (b2 e) 2 * sub_val evr (b8 e) 8 - 8 * sub_val evr (b4 e) 4 ^ 3 - 27 * sub_val evr (b6 e) 6 * sub_val evr (b6 e) 6 + 9 * sub_val evr (b2 e) 2 * sub_val evr (b4 e) 4 * sub_val evr (b6 e) 6
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


3 * 4 = 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hy
SurjVal.v evr.valtn (b4 e ^ 3) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


2 + 4 = 6
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


SurjVal.v evr.valtn (9 * b2 e) ofN 2
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


6 + 6 = 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


SurjVal.v evr.valtn (9 * b2 e * b4 e) ofN 6
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


6 + 6 = 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


SurjVal.v evr.valtn (27 * b6 e) ofN 6
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


2 + 2 = 4
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


SurjVal.v evr.valtn (-b2 e) ofN 2
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


4 + 8 = 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


SurjVal.v evr.valtn (-b2 e * b2 e) ofN 4
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hx
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hy
SurjVal.v evr.valtn (8 * b4 e ^ 3) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hx
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e - 8 * b4 e ^ 3) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hy
SurjVal.v evr.valtn (27 * b6 e * b6 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hx
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e - 8 * b4 e ^ 3 - 27 * b6 e * b6 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hy
SurjVal.v evr.valtn (9 * b2 e * b4 e * b6 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


3 * 4 = 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hy
SurjVal.v evr.valtn (b4 e ^ 3) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


2 + 4 = 6
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


SurjVal.v evr.valtn (9 * b2 e) ofN 2
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


6 + 6 = 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


SurjVal.v evr.valtn (9 * b2 e * b4 e) ofN 6
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


6 + 6 = 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


SurjVal.v evr.valtn (27 * b6 e) ofN 6
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


2 + 2 = 4
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


SurjVal.v evr.valtn (-b2 e) ofN 2
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


4 + 8 = 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


SurjVal.v evr.valtn (-b2 e * b2 e) ofN 4
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hx
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hy
SurjVal.v evr.valtn (8 * b4 e ^ 3) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hx
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e - 8 * b4 e ^ 3) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hy
SurjVal.v evr.valtn (27 * b6 e * b6 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hx
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e - 8 * b4 e ^ 3 - 27 * b6 e * b6 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hy
SurjVal.v evr.valtn (9 * b2 e * b4 e * b6 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


sub_val evr (discr e) 12 = -sub_val evr (b2 e) 2 * sub_val evr (b2 e) 2 * sub_val evr (b8 e) 8 - 8 * sub_val evr (b4 e) 4 ^ 3 - 27 * sub_val evr (b6 e) 6 * sub_val evr (b6 e) 6 + 9 * sub_val evr (b2 e) 2 * sub_val evr (b4 e) 4 * sub_val evr (b6 e) 6
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


3 * 4 = 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


3 * 4 = 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hy
SurjVal.v evr.valtn (b4 e ^ 3) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


2 + 4 = 6
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


SurjVal.v evr.valtn (9 * b2 e) ofN 2
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


6 + 6 = 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


SurjVal.v evr.valtn (9 * b2 e * b4 e) ofN 6
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


6 + 6 = 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


SurjVal.v evr.valtn (27 * b6 e) ofN 6
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


2 + 2 = 4
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


SurjVal.v evr.valtn (-b2 e) ofN 2
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


4 + 8 = 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


SurjVal.v evr.valtn (-b2 e * b2 e) ofN 4
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hx
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hy
SurjVal.v evr.valtn (8 * b4 e ^ 3) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hx
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e - 8 * b4 e ^ 3) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hy
SurjVal.v evr.valtn (27 * b6 e * b6 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hx
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e - 8 * b4 e ^ 3 - 27 * b6 e * b6 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hy
SurjVal.v evr.valtn (9 * b2 e * b4 e * b6 e) ofN 12

Goals accomplished! 🐙
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


sub_val evr (discr e) 12 = -sub_val evr (b2 e) 2 * sub_val evr (b2 e) 2 * sub_val evr (b8 e) 8 - 8 * sub_val evr (b4 e) 4 ^ 3 - 27 * sub_val evr (b6 e) 6 * sub_val evr (b6 e) 6 + 9 * sub_val evr (b2 e) 2 * sub_val evr (b4 e) 4 * sub_val evr (b6 e) 6
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hy
SurjVal.v evr.valtn (b4 e ^ 3) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hy
SurjVal.v evr.valtn (b4 e ^ 3) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


2 + 4 = 6
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


SurjVal.v evr.valtn (9 * b2 e) ofN 2
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


6 + 6 = 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


SurjVal.v evr.valtn (9 * b2 e * b4 e) ofN 6
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


6 + 6 = 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


SurjVal.v evr.valtn (27 * b6 e) ofN 6
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


2 + 2 = 4
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


SurjVal.v evr.valtn (-b2 e) ofN 2
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


4 + 8 = 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


SurjVal.v evr.valtn (-b2 e * b2 e) ofN 4
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hx
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hy
SurjVal.v evr.valtn (8 * b4 e ^ 3) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hx
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e - 8 * b4 e ^ 3) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hy
SurjVal.v evr.valtn (27 * b6 e * b6 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hx
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e - 8 * b4 e ^ 3 - 27 * b6 e * b6 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hy
SurjVal.v evr.valtn (9 * b2 e * b4 e * b6 e) ofN 12

Goals accomplished! 🐙
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


sub_val evr (discr e) 12 = -sub_val evr (b2 e) 2 * sub_val evr (b2 e) 2 * sub_val evr (b8 e) 8 - 8 * sub_val evr (b4 e) 4 ^ 3 - 27 * sub_val evr (b6 e) 6 * sub_val evr (b6 e) 6 + 9 * sub_val evr (b2 e) 2 * sub_val evr (b4 e) 4 * sub_val evr (b6 e) 6
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


2 + 4 = 6
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


2 + 4 = 6
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


SurjVal.v evr.valtn (9 * b2 e) ofN 2
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


6 + 6 = 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


SurjVal.v evr.valtn (9 * b2 e * b4 e) ofN 6
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


6 + 6 = 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


SurjVal.v evr.valtn (27 * b6 e) ofN 6
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


2 + 2 = 4
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


SurjVal.v evr.valtn (-b2 e) ofN 2
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


4 + 8 = 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


SurjVal.v evr.valtn (-b2 e * b2 e) ofN 4
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hx
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hy
SurjVal.v evr.valtn (8 * b4 e ^ 3) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hx
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e - 8 * b4 e ^ 3) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hy
SurjVal.v evr.valtn (27 * b6 e * b6 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hx
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e - 8 * b4 e ^ 3 - 27 * b6 e * b6 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hy
SurjVal.v evr.valtn (9 * b2 e * b4 e * b6 e) ofN 12

Goals accomplished! 🐙
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


sub_val evr (discr e) 12 = -sub_val evr (b2 e) 2 * sub_val evr (b2 e) 2 * sub_val evr (b8 e) 8 - 8 * sub_val evr (b4 e) 4 ^ 3 - 27 * sub_val evr (b6 e) 6 * sub_val evr (b6 e) 6 + 9 * sub_val evr (b2 e) 2 * sub_val evr (b4 e) 4 * sub_val evr (b6 e) 6
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


SurjVal.v evr.valtn (9 * b2 e) ofN 2
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


SurjVal.v evr.valtn (9 * b2 e) ofN 2
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


6 + 6 = 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


SurjVal.v evr.valtn (9 * b2 e * b4 e) ofN 6
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


6 + 6 = 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


SurjVal.v evr.valtn (27 * b6 e) ofN 6
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


2 + 2 = 4
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


SurjVal.v evr.valtn (-b2 e) ofN 2
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


4 + 8 = 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


SurjVal.v evr.valtn (-b2 e * b2 e) ofN 4
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hx
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hy
SurjVal.v evr.valtn (8 * b4 e ^ 3) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hx
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e - 8 * b4 e ^ 3) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hy
SurjVal.v evr.valtn (27 * b6 e * b6 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hx
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e - 8 * b4 e ^ 3 - 27 * b6 e * b6 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hy
SurjVal.v evr.valtn (9 * b2 e * b4 e * b6 e) ofN 12

Goals accomplished! 🐙
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


sub_val evr (discr e) 12 = -sub_val evr (b2 e) 2 * sub_val evr (b2 e) 2 * sub_val evr (b8 e) 8 - 8 * sub_val evr (b4 e) 4 ^ 3 - 27 * sub_val evr (b6 e) 6 * sub_val evr (b6 e) 6 + 9 * sub_val evr (b2 e) 2 * sub_val evr (b4 e) 4 * sub_val evr (b6 e) 6
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


6 + 6 = 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


6 + 6 = 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


SurjVal.v evr.valtn (9 * b2 e * b4 e) ofN 6
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


6 + 6 = 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


SurjVal.v evr.valtn (27 * b6 e) ofN 6
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


2 + 2 = 4
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


SurjVal.v evr.valtn (-b2 e) ofN 2
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


4 + 8 = 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


SurjVal.v evr.valtn (-b2 e * b2 e) ofN 4
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hx
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hy
SurjVal.v evr.valtn (8 * b4 e ^ 3) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hx
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e - 8 * b4 e ^ 3) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hy
SurjVal.v evr.valtn (27 * b6 e * b6 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hx
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e - 8 * b4 e ^ 3 - 27 * b6 e * b6 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hy
SurjVal.v evr.valtn (9 * b2 e * b4 e * b6 e) ofN 12

Goals accomplished! 🐙
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


sub_val evr (discr e) 12 = -sub_val evr (b2 e) 2 * sub_val evr (b2 e) 2 * sub_val evr (b8 e) 8 - 8 * sub_val evr (b4 e) 4 ^ 3 - 27 * sub_val evr (b6 e) 6 * sub_val evr (b6 e) 6 + 9 * sub_val evr (b2 e) 2 * sub_val evr (b4 e) 4 * sub_val evr (b6 e) 6
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


SurjVal.v evr.valtn (9 * b2 e * b4 e) ofN 6
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


SurjVal.v evr.valtn (9 * b2 e * b4 e) ofN 6
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


6 + 6 = 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


SurjVal.v evr.valtn (27 * b6 e) ofN 6
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


2 + 2 = 4
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


SurjVal.v evr.valtn (-b2 e) ofN 2
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


4 + 8 = 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


SurjVal.v evr.valtn (-b2 e * b2 e) ofN 4
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hx
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hy
SurjVal.v evr.valtn (8 * b4 e ^ 3) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hx
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e - 8 * b4 e ^ 3) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hy
SurjVal.v evr.valtn (27 * b6 e * b6 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hx
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e - 8 * b4 e ^ 3 - 27 * b6 e * b6 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hy
SurjVal.v evr.valtn (9 * b2 e * b4 e * b6 e) ofN 12

Goals accomplished! 🐙
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


sub_val evr (discr e) 12 = -sub_val evr (b2 e) 2 * sub_val evr (b2 e) 2 * sub_val evr (b8 e) 8 - 8 * sub_val evr (b4 e) 4 ^ 3 - 27 * sub_val evr (b6 e) 6 * sub_val evr (b6 e) 6 + 9 * sub_val evr (b2 e) 2 * sub_val evr (b4 e) 4 * sub_val evr (b6 e) 6
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


6 + 6 = 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


6 + 6 = 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


SurjVal.v evr.valtn (27 * b6 e) ofN 6
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


2 + 2 = 4
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


SurjVal.v evr.valtn (-b2 e) ofN 2
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


4 + 8 = 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


SurjVal.v evr.valtn (-b2 e * b2 e) ofN 4
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hx
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hy
SurjVal.v evr.valtn (8 * b4 e ^ 3) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hx
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e - 8 * b4 e ^ 3) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hy
SurjVal.v evr.valtn (27 * b6 e * b6 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hx
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e - 8 * b4 e ^ 3 - 27 * b6 e * b6 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hy
SurjVal.v evr.valtn (9 * b2 e * b4 e * b6 e) ofN 12

Goals accomplished! 🐙
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


sub_val evr (discr e) 12 = -sub_val evr (b2 e) 2 * sub_val evr (b2 e) 2 * sub_val evr (b8 e) 8 - 8 * sub_val evr (b4 e) 4 ^ 3 - 27 * sub_val evr (b6 e) 6 * sub_val evr (b6 e) 6 + 9 * sub_val evr (b2 e) 2 * sub_val evr (b4 e) 4 * sub_val evr (b6 e) 6
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


SurjVal.v evr.valtn (27 * b6 e) ofN 6
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


SurjVal.v evr.valtn (27 * b6 e) ofN 6
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


2 + 2 = 4
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


SurjVal.v evr.valtn (-b2 e) ofN 2
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


4 + 8 = 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


SurjVal.v evr.valtn (-b2 e * b2 e) ofN 4
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hx
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hy
SurjVal.v evr.valtn (8 * b4 e ^ 3) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hx
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e - 8 * b4 e ^ 3) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hy
SurjVal.v evr.valtn (27 * b6 e * b6 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hx
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e - 8 * b4 e ^ 3 - 27 * b6 e * b6 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hy
SurjVal.v evr.valtn (9 * b2 e * b4 e * b6 e) ofN 12

Goals accomplished! 🐙
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


sub_val evr (discr e) 12 = -sub_val evr (b2 e) 2 * sub_val evr (b2 e) 2 * sub_val evr (b8 e) 8 - 8 * sub_val evr (b4 e) 4 ^ 3 - 27 * sub_val evr (b6 e) 6 * sub_val evr (b6 e) 6 + 9 * sub_val evr (b2 e) 2 * sub_val evr (b4 e) 4 * sub_val evr (b6 e) 6
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


2 + 2 = 4
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


2 + 2 = 4
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


SurjVal.v evr.valtn (-b2 e) ofN 2
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


4 + 8 = 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


SurjVal.v evr.valtn (-b2 e * b2 e) ofN 4
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hx
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hy
SurjVal.v evr.valtn (8 * b4 e ^ 3) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hx
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e - 8 * b4 e ^ 3) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hy
SurjVal.v evr.valtn (27 * b6 e * b6 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hx
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e - 8 * b4 e ^ 3 - 27 * b6 e * b6 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hy
SurjVal.v evr.valtn (9 * b2 e * b4 e * b6 e) ofN 12

Goals accomplished! 🐙
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


sub_val evr (discr e) 12 = -sub_val evr (b2 e) 2 * sub_val evr (b2 e) 2 * sub_val evr (b8 e) 8 - 8 * sub_val evr (b4 e) 4 ^ 3 - 27 * sub_val evr (b6 e) 6 * sub_val evr (b6 e) 6 + 9 * sub_val evr (b2 e) 2 * sub_val evr (b4 e) 4 * sub_val evr (b6 e) 6
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


SurjVal.v evr.valtn (-b2 e) ofN 2
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


SurjVal.v evr.valtn (-b2 e) ofN 2
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


4 + 8 = 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


SurjVal.v evr.valtn (-b2 e * b2 e) ofN 4
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hx
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hy
SurjVal.v evr.valtn (8 * b4 e ^ 3) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hx
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e - 8 * b4 e ^ 3) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hy
SurjVal.v evr.valtn (27 * b6 e * b6 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hx
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e - 8 * b4 e ^ 3 - 27 * b6 e * b6 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hy
SurjVal.v evr.valtn (9 * b2 e * b4 e * b6 e) ofN 12

Goals accomplished! 🐙
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


sub_val evr (discr e) 12 = -sub_val evr (b2 e) 2 * sub_val evr (b2 e) 2 * sub_val evr (b8 e) 8 - 8 * sub_val evr (b4 e) 4 ^ 3 - 27 * sub_val evr (b6 e) 6 * sub_val evr (b6 e) 6 + 9 * sub_val evr (b2 e) 2 * sub_val evr (b4 e) 4 * sub_val evr (b6 e) 6
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


4 + 8 = 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


4 + 8 = 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


SurjVal.v evr.valtn (-b2 e * b2 e) ofN 4
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hx
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hy
SurjVal.v evr.valtn (8 * b4 e ^ 3) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hx
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e - 8 * b4 e ^ 3) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hy
SurjVal.v evr.valtn (27 * b6 e * b6 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hx
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e - 8 * b4 e ^ 3 - 27 * b6 e * b6 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hy
SurjVal.v evr.valtn (9 * b2 e * b4 e * b6 e) ofN 12

Goals accomplished! 🐙
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


sub_val evr (discr e) 12 = -sub_val evr (b2 e) 2 * sub_val evr (b2 e) 2 * sub_val evr (b8 e) 8 - 8 * sub_val evr (b4 e) 4 ^ 3 - 27 * sub_val evr (b6 e) 6 * sub_val evr (b6 e) 6 + 9 * sub_val evr (b2 e) 2 * sub_val evr (b4 e) 4 * sub_val evr (b6 e) 6
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


SurjVal.v evr.valtn (-b2 e * b2 e) ofN 4
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


SurjVal.v evr.valtn (-b2 e * b2 e) ofN 4
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hx
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hy
SurjVal.v evr.valtn (8 * b4 e ^ 3) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hx
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e - 8 * b4 e ^ 3) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hy
SurjVal.v evr.valtn (27 * b6 e * b6 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hx
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e - 8 * b4 e ^ 3 - 27 * b6 e * b6 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hy
SurjVal.v evr.valtn (9 * b2 e * b4 e * b6 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


SurjVal.v evr.valtn (-b2 e * b2 e) ofN 4
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


SurjVal.v evr.valtn (-b2 e) ofN 2

Goals accomplished! 🐙

Goals accomplished! 🐙
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


sub_val evr (discr e) 12 = -sub_val evr (b2 e) 2 * sub_val evr (b2 e) 2 * sub_val evr (b8 e) 8 - 8 * sub_val evr (b4 e) 4 ^ 3 - 27 * sub_val evr (b6 e) 6 * sub_val evr (b6 e) 6 + 9 * sub_val evr (b2 e) 2 * sub_val evr (b4 e) 4 * sub_val evr (b6 e) 6
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hx
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hx
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hy
SurjVal.v evr.valtn (8 * b4 e ^ 3) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hx
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e - 8 * b4 e ^ 3) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hy
SurjVal.v evr.valtn (27 * b6 e * b6 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hx
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e - 8 * b4 e ^ 3 - 27 * b6 e * b6 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hy
SurjVal.v evr.valtn (9 * b2 e * b4 e * b6 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hx
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


SurjVal.v evr.valtn (-b2 e) ofN 2

Goals accomplished! 🐙

Goals accomplished! 🐙
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


sub_val evr (discr e) 12 = -sub_val evr (b2 e) 2 * sub_val evr (b2 e) 2 * sub_val evr (b8 e) 8 - 8 * sub_val evr (b4 e) 4 ^ 3 - 27 * sub_val evr (b6 e) 6 * sub_val evr (b6 e) 6 + 9 * sub_val evr (b2 e) 2 * sub_val evr (b4 e) 4 * sub_val evr (b6 e) 6
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hy
SurjVal.v evr.valtn (8 * b4 e ^ 3) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hy
SurjVal.v evr.valtn (8 * b4 e ^ 3) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hx
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e - 8 * b4 e ^ 3) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hy
SurjVal.v evr.valtn (27 * b6 e * b6 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hx
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e - 8 * b4 e ^ 3 - 27 * b6 e * b6 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hy
SurjVal.v evr.valtn (9 * b2 e * b4 e * b6 e) ofN 12

Goals accomplished! 🐙
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


sub_val evr (discr e) 12 = -sub_val evr (b2 e) 2 * sub_val evr (b2 e) 2 * sub_val evr (b8 e) 8 - 8 * sub_val evr (b4 e) 4 ^ 3 - 27 * sub_val evr (b6 e) 6 * sub_val evr (b6 e) 6 + 9 * sub_val evr (b2 e) 2 * sub_val evr (b4 e) 4 * sub_val evr (b6 e) 6
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hx
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e - 8 * b4 e ^ 3) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hx
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e - 8 * b4 e ^ 3) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hy
SurjVal.v evr.valtn (27 * b6 e * b6 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hx
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e - 8 * b4 e ^ 3 - 27 * b6 e * b6 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hy
SurjVal.v evr.valtn (9 * b2 e * b4 e * b6 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hx.ha
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hx.hb
SurjVal.v evr.valtn (8 * b4 e ^ 3) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hx
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e - 8 * b4 e ^ 3) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hy
SurjVal.v evr.valtn (27 * b6 e * b6 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hx
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e - 8 * b4 e ^ 3 - 27 * b6 e * b6 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hy
SurjVal.v evr.valtn (9 * b2 e * b4 e * b6 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hx.ha
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hx.ha
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hx.hb
SurjVal.v evr.valtn (8 * b4 e ^ 3) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hx.ha
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


SurjVal.v evr.valtn (-b2 e) ofN 2

Goals accomplished! 🐙

Goals accomplished! 🐙
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hx
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e - 8 * b4 e ^ 3) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hy
SurjVal.v evr.valtn (27 * b6 e * b6 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hx
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e - 8 * b4 e ^ 3 - 27 * b6 e * b6 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hy
SurjVal.v evr.valtn (9 * b2 e * b4 e * b6 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hx.hb
SurjVal.v evr.valtn (8 * b4 e ^ 3) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hx.hb
SurjVal.v evr.valtn (8 * b4 e ^ 3) ofN 12

Goals accomplished! 🐙
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


sub_val evr (discr e) 12 = -sub_val evr (b2 e) 2 * sub_val evr (b2 e) 2 * sub_val evr (b8 e) 8 - 8 * sub_val evr (b4 e) 4 ^ 3 - 27 * sub_val evr (b6 e) 6 * sub_val evr (b6 e) 6 + 9 * sub_val evr (b2 e) 2 * sub_val evr (b4 e) 4 * sub_val evr (b6 e) 6
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hy
SurjVal.v evr.valtn (27 * b6 e * b6 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hy
SurjVal.v evr.valtn (27 * b6 e * b6 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hx
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e - 8 * b4 e ^ 3 - 27 * b6 e * b6 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hy
SurjVal.v evr.valtn (9 * b2 e * b4 e * b6 e) ofN 12

Goals accomplished! 🐙
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


sub_val evr (discr e) 12 = -sub_val evr (b2 e) 2 * sub_val evr (b2 e) 2 * sub_val evr (b8 e) 8 - 8 * sub_val evr (b4 e) 4 ^ 3 - 27 * sub_val evr (b6 e) 6 * sub_val evr (b6 e) 6 + 9 * sub_val evr (b2 e) 2 * sub_val evr (b4 e) 4 * sub_val evr (b6 e) 6
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hx
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e - 8 * b4 e ^ 3 - 27 * b6 e * b6 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hx
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e - 8 * b4 e ^ 3 - 27 * b6 e * b6 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hy
SurjVal.v evr.valtn (9 * b2 e * b4 e * b6 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hx.ha
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e - 8 * b4 e ^ 3) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hx.hb
SurjVal.v evr.valtn (27 * b6 e * b6 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hx
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e - 8 * b4 e ^ 3 - 27 * b6 e * b6 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hy
SurjVal.v evr.valtn (9 * b2 e * b4 e * b6 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hx.ha
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e - 8 * b4 e ^ 3) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hx.ha
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e - 8 * b4 e ^ 3) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hx.hb
SurjVal.v evr.valtn (27 * b6 e * b6 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hx.ha.ha
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hx.ha.hb
SurjVal.v evr.valtn (8 * b4 e ^ 3) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hx.ha
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e - 8 * b4 e ^ 3) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hx.hb
SurjVal.v evr.valtn (27 * b6 e * b6 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hx.ha.ha
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hx.ha.hb
SurjVal.v evr.valtn (8 * b4 e ^ 3) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


SurjVal.v evr.valtn (-b2 e) ofN 2

Goals accomplished! 🐙
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hx.ha.hb
SurjVal.v evr.valtn (8 * b4 e ^ 3) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hx.ha
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e - 8 * b4 e ^ 3) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hx.hb
SurjVal.v evr.valtn (27 * b6 e * b6 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hx.ha.hb
SurjVal.v evr.valtn (b4 e ^ 3) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hx.ha
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e - 8 * b4 e ^ 3) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hx.hb
SurjVal.v evr.valtn (27 * b6 e * b6 e) ofN 12

Goals accomplished! 🐙
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hx
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e - 8 * b4 e ^ 3 - 27 * b6 e * b6 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hy
SurjVal.v evr.valtn (9 * b2 e * b4 e * b6 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hx.hb
SurjVal.v evr.valtn (27 * b6 e * b6 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hx.hb
SurjVal.v evr.valtn (27 * b6 e * b6 e) ofN 12

Goals accomplished! 🐙
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


sub_val evr (discr e) 12 = -sub_val evr (b2 e) 2 * sub_val evr (b2 e) 2 * sub_val evr (b8 e) 8 - 8 * sub_val evr (b4 e) 4 ^ 3 - 27 * sub_val evr (b6 e) 6 * sub_val evr (b6 e) 6 + 9 * sub_val evr (b2 e) 2 * sub_val evr (b4 e) 4 * sub_val evr (b6 e) 6
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hy
SurjVal.v evr.valtn (9 * b2 e * b4 e * b6 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hy
SurjVal.v evr.valtn (9 * b2 e * b4 e * b6 e) ofN 12

Goals accomplished! 🐙
lemma
b2_of_pi_scaling: ∀ (evr : EnatValRing p) (e : Model R), SurjVal.v evr.valtn e.a1 ofN 1SurjVal.v evr.valtn e.a2 ofN 2b2 (pi_scaling evr e) = EnatValRing.sub_val evr (b2 e) 2
b2_of_pi_scaling
(evr :
EnatValRing: {R : Type ?u.12066} → R[inst : IntegralDomain R] → Type ?u.12066
EnatValRing
p: R
p
) (
e: Model R
e
:
Model: (R : Type ?u.12074) → [inst : IntegralDomain R] → Type ?u.12074
Model
R: Type u
R
) (
h1: SurjVal.v evr.valtn e.a1 ofN 1
h1
: evr.
valtn: {R : Type ?u.12079} → {p : R} → [inst : IntegralDomain R] → EnatValRing pSurjVal p
valtn
.
v: {R : Type ?u.12086} → {p : R} → [inst : IntegralDomain R] → SurjVal pRℕ∪∞
v
e: Model R
e
.
a1: {R : Type ?u.12093} → [inst : IntegralDomain R] → Model RR
a1
ofN: ℕ∪∞
ofN
1: ?m.12099
1
) (
h2: SurjVal.v evr.valtn e.a2 ofN 2
h2
: evr.
valtn: {R : Type ?u.12117} → {p : R} → [inst : IntegralDomain R] → EnatValRing pSurjVal p
valtn
.
v: {R : Type ?u.12121} → {p : R} → [inst : IntegralDomain R] → SurjVal pRℕ∪∞
v
e: Model R
e
.
a2: {R : Type ?u.12125} → [inst : IntegralDomain R] → Model RR
a2
ofN: ℕ∪∞
ofN
2: ?m.12129
2
) : (
pi_scaling: {R : Type ?u.12139} → [inst : IntegralDomain R] → {p : R} → EnatValRing pModel RModel R
pi_scaling
evr
e: Model R
e
).
b2: {R : Type ?u.12146} → [inst : IntegralDomain R] → Model RR
b2
= evr.
sub_val: {R : Type ?u.12152} → [inst : IntegralDomain R] → {p : R} → EnatValRing pRR
sub_val
e: Model R
e
.
b2: {R : Type ?u.12162} → [inst : IntegralDomain R] → Model RR
b2
2: ?m.12169
2
:=
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2


R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2


EnatValRing.sub_val evr e.a1 1 * EnatValRing.sub_val evr e.a1 1 + 4 * EnatValRing.sub_val evr e.a2 2 = EnatValRing.sub_val evr (e.a1 * e.a1 + 4 * e.a2) 2
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2



Goals accomplished! 🐙
lemma
b4_of_pi_scaling: ∀ (evr : EnatValRing p) (e : Model R), SurjVal.v evr.valtn e.a1 ofN 1SurjVal.v evr.valtn e.a3 ofN 3SurjVal.v evr.valtn e.a4 ofN 4b4 (pi_scaling evr e) = EnatValRing.sub_val evr (b4 e) 4
b4_of_pi_scaling
(evr :
EnatValRing: {R : Type ?u.12434} → R[inst : IntegralDomain R] → Type ?u.12434
EnatValRing
p: R
p
) (
e: Model R
e
:
Model: (R : Type ?u.12442) → [inst : IntegralDomain R] → Type ?u.12442
Model
R: Type u
R
) (
h1: SurjVal.v evr.valtn e.a1 ofN 1
h1
: evr.
valtn: {R : Type ?u.12447} → {p : R} → [inst : IntegralDomain R] → EnatValRing pSurjVal p
valtn
.
v: {R : Type ?u.12454} → {p : R} → [inst : IntegralDomain R] → SurjVal pRℕ∪∞
v
e: Model R
e
.
a1: {R : Type ?u.12461} → [inst : IntegralDomain R] → Model RR
a1
ofN: ℕ∪∞
ofN
1: ?m.12467
1
) (
h3: SurjVal.v evr.valtn e.a3 ofN 3
h3
: evr.
valtn: {R : Type ?u.12485} → {p : R} → [inst : IntegralDomain R] → EnatValRing pSurjVal p
valtn
.
v: {R : Type ?u.12489} → {p : R} → [inst : IntegralDomain R] → SurjVal pRℕ∪∞
v
e: Model R
e
.
a3: {R : Type ?u.12493} → [inst : IntegralDomain R] → Model RR
a3
ofN: ℕ∪∞
ofN
3: ?m.12497
3
) (
h4: SurjVal.v evr.valtn e.a4 ofN 4
h4
: evr.
valtn: {R : Type ?u.12507} → {p : R} → [inst : IntegralDomain R] → EnatValRing pSurjVal p
valtn
.
v: {R : Type ?u.12511} → {p : R} → [inst : IntegralDomain R] → SurjVal pRℕ∪∞
v
e: Model R
e
.
a4: {R : Type ?u.12515} → [inst : IntegralDomain R] → Model RR
a4
ofN: ℕ∪∞
ofN
4: ?m.12519
4
) : (
pi_scaling: {R : Type ?u.12529} → [inst : IntegralDomain R] → {p : R} → EnatValRing pModel RModel R
pi_scaling
evr
e: Model R
e
).
b4: {R : Type ?u.12536} → [inst : IntegralDomain R] → Model RR
b4
= evr.
sub_val: {R : Type ?u.12542} → [inst : IntegralDomain R] → {p : R} → EnatValRing pRR
sub_val
e: Model R
e
.
b4: {R : Type ?u.12552} → [inst : IntegralDomain R] → Model RR
b4
4: ?m.12559
4
:=
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4


R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4


EnatValRing.sub_val evr e.a1 1 * EnatValRing.sub_val evr e.a3 3 + 2 * EnatValRing.sub_val evr e.a4 4 = EnatValRing.sub_val evr (e.a1 * e.a3 + 2 * e.a4) 4
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4



Goals accomplished! 🐙
lemma
b6_of_pi_scaling: ∀ {R : Type u} [inst : IntegralDomain R] {p : R} (evr : EnatValRing p) (e : Model R), SurjVal.v evr.valtn e.a3 ofN 3SurjVal.v evr.valtn e.a6 ofN 6b6 (pi_scaling evr e) = EnatValRing.sub_val evr (b6 e) 6
b6_of_pi_scaling
(evr :
EnatValRing: {R : Type ?u.12826} → R[inst : IntegralDomain R] → Type ?u.12826
EnatValRing
p: R
p
) (
e: Model R
e
:
Model: (R : Type ?u.12834) → [inst : IntegralDomain R] → Type ?u.12834
Model
R: Type u
R
) (
h3: SurjVal.v evr.valtn e.a3 ofN 3
h3
: evr.
valtn: {R : Type ?u.12839} → {p : R} → [inst : IntegralDomain R] → EnatValRing pSurjVal p
valtn
.
v: {R : Type ?u.12846} → {p : R} → [inst : IntegralDomain R] → SurjVal pRℕ∪∞
v
e: Model R
e
.
a3: {R : Type ?u.12853} → [inst : IntegralDomain R] → Model RR
a3
ofN: ℕ∪∞
ofN
3: ?m.12859
3
) (
h6: SurjVal.v evr.valtn e.a6 ofN 6
h6
: evr.
valtn: {R : Type ?u.12876} → {p : R} → [inst : IntegralDomain R] → EnatValRing pSurjVal p
valtn
.
v: {R : Type ?u.12880} → {p : R} → [inst : IntegralDomain R] → SurjVal pRℕ∪∞
v
e: Model R
e
.
a6: {R : Type ?u.12884} → [inst : IntegralDomain R] → Model RR
a6
ofN: ℕ∪∞
ofN
6: ?m.12888
6
) : (
pi_scaling: {R : Type ?u.12898} → [inst : IntegralDomain R] → {p : R} → EnatValRing pModel RModel R
pi_scaling
evr
e: Model R
e
).
b6: {R : Type ?u.12905} → [inst : IntegralDomain R] → Model RR
b6
= evr.
sub_val: {R : Type ?u.12911} → [inst : IntegralDomain R] → {p : R} → EnatValRing pRR
sub_val
e: Model R
e
.
b6: {R : Type ?u.12921} → [inst : IntegralDomain R] → Model RR
b6
6: ?m.12928
6
:=
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h3: SurjVal.v evr.valtn e.a3 ofN 3

h6: SurjVal.v evr.valtn e.a6 ofN 6


R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h3: SurjVal.v evr.valtn e.a3 ofN 3

h6: SurjVal.v evr.valtn e.a6 ofN 6


EnatValRing.sub_val evr e.a3 3 * EnatValRing.sub_val evr e.a3 3 + 4 * EnatValRing.sub_val evr e.a6 6 = EnatValRing.sub_val evr (e.a3 * e.a3 + 4 * e.a6) 6
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h3: SurjVal.v evr.valtn e.a3 ofN 3

h6: SurjVal.v evr.valtn e.a6 ofN 6



Goals accomplished! 🐙
lemma
b8_of_pi_scaling: ∀ {R : Type u} [inst : IntegralDomain R] {p : R} (evr : EnatValRing p) (e : Model R), SurjVal.v evr.valtn e.a1 ofN 1SurjVal.v evr.valtn e.a2 ofN 2SurjVal.v evr.valtn e.a3 ofN 3SurjVal.v evr.valtn e.a4 ofN 4SurjVal.v evr.valtn e.a6 ofN 6b8 (pi_scaling evr e) = EnatValRing.sub_val evr (b8 e) 8
b8_of_pi_scaling
(evr :
EnatValRing: {R : Type ?u.13193} → R[inst : IntegralDomain R] → Type ?u.13193
EnatValRing
p: R
p
) (
e: Model R
e
:
Model: (R : Type ?u.13201) → [inst : IntegralDomain R] → Type ?u.13201
Model
R: Type u
R
) (
h1: SurjVal.v evr.valtn e.a1 ofN 1
h1
: evr.
valtn: {R : Type ?u.13206} → {p : R} → [inst : IntegralDomain R] → EnatValRing pSurjVal p
valtn
.
v: {R : Type ?u.13213} → {p : R} → [inst : IntegralDomain R] → SurjVal pRℕ∪∞
v
e: Model R
e
.
a1: {R : Type ?u.13220} → [inst : IntegralDomain R] → Model RR
a1
ofN: ℕ∪∞
ofN
1: ?m.13226
1
) (
h2: SurjVal.v evr.valtn e.a2 ofN 2
h2
: evr.
valtn: {R : Type ?u.13244} → {p : R} → [inst : IntegralDomain R] → EnatValRing pSurjVal p
valtn
.
v: {R : Type ?u.13248} → {p : R} → [inst : IntegralDomain R] → SurjVal pRℕ∪∞
v
e: Model R
e
.
a2: {R : Type ?u.13252} → [inst : IntegralDomain R] → Model RR
a2
ofN: ℕ∪∞
ofN
2: ?m.13256
2
) (
h3: SurjVal.v evr.valtn e.a3 ofN 3
h3
: evr.
valtn: {R : Type ?u.13266} → {p : R} → [inst : IntegralDomain R] → EnatValRing pSurjVal p
valtn
.
v: {R : Type ?u.13270} → {p : R} → [inst : IntegralDomain R] → SurjVal pRℕ∪∞
v
e: Model R
e
.
a3: {R : Type ?u.13274} → [inst : IntegralDomain R] → Model RR
a3
ofN: ℕ∪∞
ofN
3: ?m.13278
3
) (
h4: SurjVal.v evr.valtn e.a4 ofN 4
h4
: evr.
valtn: {R : Type ?u.13288} → {p : R} → [inst : IntegralDomain R] → EnatValRing pSurjVal p
valtn
.
v: {R : Type ?u.13292} → {p : R} → [inst : IntegralDomain R] → SurjVal pRℕ∪∞
v
e: Model R
e
.
a4: {R : Type ?u.13296} → [inst : IntegralDomain R] → Model RR
a4
ofN: ℕ∪∞
ofN
4: ?m.13300
4
) (
h6: SurjVal.v evr.valtn e.a6 ofN 6
h6
: evr.
valtn: {R : Type ?u.13310} → {p : R} → [inst : IntegralDomain R] → EnatValRing pSurjVal p
valtn
.
v: {R : Type ?u.13314} → {p : R} → [inst : IntegralDomain R] → SurjVal pRℕ∪∞
v
e: Model R
e
.
a6: {R : Type ?u.13318} → [inst : IntegralDomain R] → Model RR
a6
ofN: ℕ∪∞
ofN
6: ?m.13322
6
) : (
pi_scaling: {R : Type ?u.13332} → [inst : IntegralDomain R] → {p : R} → EnatValRing pModel RModel R
pi_scaling
evr
e: Model R
e
).
b8: {R : Type ?u.13339} → [inst : IntegralDomain R] → Model RR
b8
= evr.
sub_val: {R : Type ?u.13345} → [inst : IntegralDomain R] → {p : R} → EnatValRing pRR
sub_val
e: Model R
e
.
b8: {R : Type ?u.13355} → [inst : IntegralDomain R] → Model RR
b8
8: ?m.13362
8
:=
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


EnatValRing.sub_val evr e.a1 1 * EnatValRing.sub_val evr e.a1 1 * EnatValRing.sub_val evr e.a6 6 - EnatValRing.sub_val evr e.a1 1 * EnatValRing.sub_val evr e.a3 3 * EnatValRing.sub_val evr e.a4 4 + 4 * EnatValRing.sub_val evr e.a2 2 * EnatValRing.sub_val evr e.a6 6 + EnatValRing.sub_val evr e.a2 2 * EnatValRing.sub_val evr e.a3 3 * EnatValRing.sub_val evr e.a3 3 - EnatValRing.sub_val evr e.a4 4 * EnatValRing.sub_val evr e.a4 4 = EnatValRing.sub_val evr (e.a1 * e.a1 * e.a6 - e.a1 * e.a3 * e.a4 + 4 * e.a2 * e.a6 + e.a2 * e.a3 * e.a3 - e.a4 * e.a4) 8
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6



Goals accomplished! 🐙
lemma
val_b2_of_val_a12: ∀ (evr : EnatValRing p) (e : Model R), SurjVal.v evr.valtn e.a1 ofN 1SurjVal.v evr.valtn e.a2 ofN 2SurjVal.v evr.valtn (b2 e) ofN 2
val_b2_of_val_a12
(evr :
EnatValRing: {R : Type ?u.13668} → R[inst : IntegralDomain R] → Type ?u.13668
EnatValRing
p: R
p
) (
e: Model R
e
:
Model: (R : Type ?u.13676) → [inst : IntegralDomain R] → Type ?u.13676
Model
R: Type u
R
) (
h1: SurjVal.v evr.valtn e.a1 ofN 1
h1
: evr.
valtn: {R : Type ?u.13681} → {p : R} → [inst : IntegralDomain R] → EnatValRing pSurjVal p
valtn
.
v: {R : Type ?u.13688} → {p : R} → [inst : IntegralDomain R] → SurjVal pRℕ∪∞
v
e: Model R
e
.
a1: {R : Type ?u.13695} → [inst : IntegralDomain R] → Model RR
a1
ofN: ℕ∪∞
ofN
1: ?m.13701
1
) (
h2: SurjVal.v evr.valtn e.a2 ofN 2
h2
: evr.
valtn: {R : Type ?u.13719} → {p : R} → [inst : IntegralDomain R] → EnatValRing pSurjVal p
valtn
.
v: {R : Type ?u.13723} → {p : R} → [inst : IntegralDomain R] → SurjVal pRℕ∪∞
v
e: Model R
e
.
a2: {R : Type ?u.13727} → [inst : IntegralDomain R] → Model RR
a2
ofN: ℕ∪∞
ofN
2: ?m.13731
2
) : evr.
valtn: {R : Type ?u.13741} → {p : R} → [inst : IntegralDomain R] → EnatValRing pSurjVal p
valtn
.
v: {R : Type ?u.13745} → {p : R} → [inst : IntegralDomain R] → SurjVal pRℕ∪∞
v
e: Model R
e
.
b2: {R : Type ?u.13749} → [inst : IntegralDomain R] → Model RR
b2
ofN: ℕ∪∞
ofN
2: ?m.13756
2
:=
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2


SurjVal.v evr.valtn (b2 e) ofN 2
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2


SurjVal.v evr.valtn (e.a1 * e.a1 + 4 * e.a2) ofN 2
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2


SurjVal.v evr.valtn (b2 e) ofN 2
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2


ha
SurjVal.v evr.valtn (e.a1 * e.a1) ofN 2
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2


hb
SurjVal.v evr.valtn (4 * e.a2) ofN 2
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2


SurjVal.v evr.valtn (b2 e) ofN 2
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2


ha
SurjVal.v evr.valtn (e.a1 * e.a1) ofN 2
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2


ha
SurjVal.v evr.valtn (e.a1 * e.a1) ofN 2
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2


hb
SurjVal.v evr.valtn (4 * e.a2) ofN 2

Goals accomplished! 🐙
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2


SurjVal.v evr.valtn (b2 e) ofN 2
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2


hb
SurjVal.v evr.valtn (4 * e.a2) ofN 2
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2


hb
SurjVal.v evr.valtn (4 * e.a2) ofN 2

Goals accomplished! 🐙
lemma
val_b4_of_val_a134: ∀ (evr : EnatValRing p) (e : Model R), SurjVal.v evr.valtn e.a1 ofN 1SurjVal.v evr.valtn e.a3 ofN 3SurjVal.v evr.valtn e.a4 ofN 4SurjVal.v evr.valtn (b4 e) ofN 4
val_b4_of_val_a134
(evr :
EnatValRing: {R : Type ?u.14036} → R[inst : IntegralDomain R] → Type ?u.14036
EnatValRing
p: R
p
) (
e: Model R
e
:
Model: (R : Type ?u.14044) → [inst : IntegralDomain R] → Type ?u.14044
Model
R: Type u
R
) (
h1: SurjVal.v evr.valtn e.a1 ofN 1
h1
: evr.
valtn: {R : Type ?u.14049} → {p : R} → [inst : IntegralDomain R] → EnatValRing pSurjVal p
valtn
.
v: {R : Type ?u.14056} → {p : R} → [inst : IntegralDomain R] → SurjVal pRℕ∪∞
v
e: Model R
e
.
a1: {R : Type ?u.14063} → [inst : IntegralDomain R] → Model RR
a1
ofN: ℕ∪∞
ofN
1: ?m.14069
1
) (
h3: SurjVal.v evr.valtn e.a3 ofN 3
h3
: evr.
valtn: {R : Type ?u.14087} → {p : R} → [inst : IntegralDomain R] → EnatValRing pSurjVal p
valtn
.
v: {R : Type ?u.14091} → {p : R} → [inst : IntegralDomain R] → SurjVal pRℕ∪∞
v
e: Model R
e
.
a3: {R : Type ?u.14095} → [inst : IntegralDomain R] → Model RR
a3
ofN: ℕ∪∞
ofN
3: ?m.14099
3
) (
h4: SurjVal.v evr.valtn e.a4 ofN 4
h4
: evr.
valtn: {R : Type ?u.14109} → {p : R} → [inst : IntegralDomain R] → EnatValRing pSurjVal p
valtn
.
v: {R : Type ?u.14113} → {p : R} → [inst : IntegralDomain R] → SurjVal pRℕ∪∞
v
e: Model R
e
.
a4: {R : Type ?u.14117} → [inst : IntegralDomain R] → Model RR
a4
ofN: ℕ∪∞
ofN
4: ?m.14121
4
) : evr.
valtn: {R : Type ?u.14131} → {p : R} → [inst : IntegralDomain R] → EnatValRing pSurjVal p
valtn
.
v: {R : Type ?u.14135} → {p : R} → [inst : IntegralDomain R] → SurjVal pRℕ∪∞
v
e: Model R
e
.
b4: {R : Type ?u.14139} → [inst : IntegralDomain R] → Model RR
b4
ofN: ℕ∪∞
ofN
4: ?m.14146
4
:=
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4


SurjVal.v evr.valtn (b4 e) ofN 4
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4


SurjVal.v evr.valtn (e.a1 * e.a3 + 2 * e.a4) ofN 4
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4


SurjVal.v evr.valtn (b4 e) ofN 4
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4


ha
SurjVal.v evr.valtn (e.a1 * e.a3) ofN 4
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4


hb
SurjVal.v evr.valtn (2 * e.a4) ofN 4
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4


SurjVal.v evr.valtn (b4 e) ofN 4
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4


ha
SurjVal.v evr.valtn (e.a1 * e.a3) ofN 4
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4


ha
SurjVal.v evr.valtn (e.a1 * e.a3) ofN 4
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4


hb
SurjVal.v evr.valtn (2 * e.a4) ofN 4

Goals accomplished! 🐙
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4


SurjVal.v evr.valtn (b4 e) ofN 4
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4


hb
SurjVal.v evr.valtn (2 * e.a4) ofN 4
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4


hb
SurjVal.v evr.valtn (2 * e.a4) ofN 4

Goals accomplished! 🐙
lemma
val_b6_of_val_a36: ∀ (evr : EnatValRing p) (e : Model R), SurjVal.v evr.valtn e.a3 ofN 3SurjVal.v evr.valtn e.a6 ofN 6SurjVal.v evr.valtn (b6 e) ofN 6
val_b6_of_val_a36
(evr :
EnatValRing: {R : Type ?u.14435} → R[inst : IntegralDomain R] → Type ?u.14435
EnatValRing
p: R
p
) (
e: Model R
e
:
Model: (R : Type ?u.14443) → [inst : IntegralDomain R] → Type ?u.14443
Model
R: Type u
R
) (
h3: SurjVal.v evr.valtn e.a3 ofN 3
h3
: evr.
valtn: {R : Type ?u.14448} → {p : R} → [inst : IntegralDomain R] → EnatValRing pSurjVal p
valtn
.
v: {R : Type ?u.14455} → {p : R} → [inst : IntegralDomain R] → SurjVal pRℕ∪∞
v
e: Model R
e
.
a3: {R : Type ?u.14462} → [inst : IntegralDomain R] → Model RR
a3
ofN: ℕ∪∞
ofN
3: ?m.14468
3
) (
h6: SurjVal.v evr.valtn e.a6 ofN 6
h6
: evr.
valtn: {R : Type ?u.14485} → {p : R} → [inst : IntegralDomain R] → EnatValRing pSurjVal p
valtn
.
v: {R : Type ?u.14489} → {p : R} → [inst : IntegralDomain R] → SurjVal pRℕ∪∞
v
e: Model R
e
.
a6: {R : Type ?u.14493} → [inst : IntegralDomain R] → Model RR
a6
ofN: ℕ∪∞
ofN
6: ?m.14497
6
) : evr.
valtn: {R : Type ?u.14507} → {p : R} → [inst : IntegralDomain R] → EnatValRing pSurjVal p
valtn
.
v: {R : Type ?u.14511} → {p : R} → [inst : IntegralDomain R] → SurjVal pRℕ∪∞
v
e: Model R
e
.
b6: {R : Type ?u.14515} → [inst : IntegralDomain R] → Model RR
b6
ofN: ℕ∪∞
ofN
6: ?m.14522
6
:=
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h3: SurjVal.v evr.valtn e.a3 ofN 3

h6: SurjVal.v evr.valtn e.a6 ofN 6


SurjVal.v evr.valtn (b6 e) ofN 6
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h3: SurjVal.v evr.valtn e.a3 ofN 3

h6: SurjVal.v evr.valtn e.a6 ofN 6


SurjVal.v evr.valtn (e.a3 * e.a3 + 4 * e.a6) ofN 6
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h3: SurjVal.v evr.valtn e.a3 ofN 3

h6: SurjVal.v evr.valtn e.a6 ofN 6


SurjVal.v evr.valtn (b6 e) ofN 6
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h3: SurjVal.v evr.valtn e.a3 ofN 3

h6: SurjVal.v evr.valtn e.a6 ofN 6


ha
SurjVal.v evr.valtn (e.a3 * e.a3) ofN 6
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h3: SurjVal.v evr.valtn e.a3 ofN 3

h6: SurjVal.v evr.valtn e.a6 ofN 6


hb
SurjVal.v evr.valtn (4 * e.a6) ofN 6
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h3: SurjVal.v evr.valtn e.a3 ofN 3

h6: SurjVal.v evr.valtn e.a6 ofN 6


SurjVal.v evr.valtn (b6 e) ofN 6
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h3: SurjVal.v evr.valtn e.a3 ofN 3

h6: SurjVal.v evr.valtn e.a6 ofN 6


ha
SurjVal.v evr.valtn (e.a3 * e.a3) ofN 6
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h3: SurjVal.v evr.valtn e.a3 ofN 3

h6: SurjVal.v evr.valtn e.a6 ofN 6


ha
SurjVal.v evr.valtn (e.a3 * e.a3) ofN 6
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h3: SurjVal.v evr.valtn e.a3 ofN 3

h6: SurjVal.v evr.valtn e.a6 ofN 6


hb
SurjVal.v evr.valtn (4 * e.a6) ofN 6

Goals accomplished! 🐙
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h3: SurjVal.v evr.valtn e.a3 ofN 3

h6: SurjVal.v evr.valtn e.a6 ofN 6


SurjVal.v evr.valtn (b6 e) ofN 6
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h3: SurjVal.v evr.valtn e.a3 ofN 3

h6: SurjVal.v evr.valtn e.a6 ofN 6


hb
SurjVal.v evr.valtn (4 * e.a6) ofN 6
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h3: SurjVal.v evr.valtn e.a3 ofN 3

h6: SurjVal.v evr.valtn e.a6 ofN 6


hb
SurjVal.v evr.valtn (4 * e.a6) ofN 6

Goals accomplished! 🐙
lemma
val_b8_of_val_ai: ∀ {R : Type u} [inst : IntegralDomain R] {p : R} (evr : EnatValRing p) (e : Model R), SurjVal.v evr.valtn e.a1 ofN 1SurjVal.v evr.valtn e.a2 ofN 2SurjVal.v evr.valtn e.a3 ofN 3SurjVal.v evr.valtn e.a4 ofN 4SurjVal.v evr.valtn e.a6 ofN 6SurjVal.v evr.valtn (b8 e) ofN 8
val_b8_of_val_ai
(evr :
EnatValRing: {R : Type ?u.14802} → R[inst : IntegralDomain R] → Type ?u.14802
EnatValRing
p: R
p
) (
e: Model R
e
:
Model: (R : Type ?u.14810) → [inst : IntegralDomain R] → Type ?u.14810
Model
R: Type u
R
) (
h1: SurjVal.v evr.valtn e.a1 ofN 1
h1
: evr.
valtn: {R : Type ?u.14815} → {p : R} → [inst : IntegralDomain R] → EnatValRing pSurjVal p
valtn
.
v: {R : Type ?u.14822} → {p : R} → [inst : IntegralDomain R] → SurjVal pRℕ∪∞
v
e: Model R
e
.
a1: {R : Type ?u.14829} → [inst : IntegralDomain R] → Model RR
a1
ofN: ℕ∪∞
ofN
1: ?m.14835
1
) (
h2: SurjVal.v evr.valtn e.a2 ofN 2
h2
: evr.
valtn: {R : Type ?u.14853} → {p : R} → [inst : IntegralDomain R] → EnatValRing pSurjVal p
valtn
.
v: {R : Type ?u.14857} → {p : R} → [inst : IntegralDomain R] → SurjVal pRℕ∪∞
v
e: Model R
e
.
a2: {R : Type ?u.14861} → [inst : IntegralDomain R] → Model RR
a2
ofN: ℕ∪∞
ofN
2: ?m.14865
2
) (
h3: SurjVal.v evr.valtn e.a3 ofN 3
h3
: evr.
valtn: {R : Type ?u.14875} → {p : R} → [inst : IntegralDomain R] → EnatValRing pSurjVal p
valtn
.
v: {R : Type ?u.14879} → {p : R} → [inst : IntegralDomain R] → SurjVal pRℕ∪∞
v
e: Model R
e
.
a3: {R : Type ?u.14883} → [inst : IntegralDomain R] → Model RR
a3
ofN: ℕ∪∞
ofN
3: ?m.14887
3
) (
h4: SurjVal.v evr.valtn e.a4 ofN 4
h4
: evr.
valtn: {R : Type ?u.14897} → {p : R} → [inst : IntegralDomain R] → EnatValRing pSurjVal p
valtn
.
v: {R : Type ?u.14901} → {p : R} → [inst : IntegralDomain R] → SurjVal pRℕ∪∞
v
e: Model R
e
.
a4: {R : Type ?u.14905} → [inst : IntegralDomain R] → Model RR
a4
ofN: ℕ∪∞
ofN
4: ?m.14909
4
) (
h6: SurjVal.v evr.valtn e.a6 ofN 6
h6
: evr.
valtn: {R : Type ?u.14919} → {p : R} → [inst : IntegralDomain R] → EnatValRing pSurjVal p
valtn
.
v: {R : Type ?u.14923} → {p : R} → [inst : IntegralDomain R] → SurjVal pRℕ∪∞
v
e: Model R
e
.
a6: {R : Type ?u.14927} → [inst : IntegralDomain R] → Model RR
a6
ofN: ℕ∪∞
ofN
6: ?m.14931
6
) : evr.
valtn: {R : Type ?u.14941} → {p : R} → [inst : IntegralDomain R] → EnatValRing pSurjVal p
valtn
.
v: {R : Type ?u.14945} → {p : R} → [inst : IntegralDomain R] → SurjVal pRℕ∪∞
v
e: Model R
e
.
b8: {R : Type ?u.14949} → [inst : IntegralDomain R] → Model RR
b8
ofN: ℕ∪∞
ofN
8: ?m.14956
8
:=
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


SurjVal.v evr.valtn (b8 e) ofN 8
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6 + -(e.a1 * e.a3 * e.a4) + 4 * e.a2 * e.a6 + e.a2 * e.a3 * e.a3 + -(e.a4 * e.a4)) ofN 8
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


SurjVal.v evr.valtn (b8 e) ofN 8
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


ha
SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6 + -(e.a1 * e.a3 * e.a4) + 4 * e.a2 * e.a6 + e.a2 * e.a3 * e.a3) ofN 8
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


hb
SurjVal.v evr.valtn (-(e.a4 * e.a4)) ofN 8
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


SurjVal.v evr.valtn (b8 e) ofN 8
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


ha
SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6 + -(e.a1 * e.a3 * e.a4) + 4 * e.a2 * e.a6 + e.a2 * e.a3 * e.a3) ofN 8
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


ha
SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6 + -(e.a1 * e.a3 * e.a4) + 4 * e.a2 * e.a6 + e.a2 * e.a3 * e.a3) ofN 8
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


hb
SurjVal.v evr.valtn (-(e.a4 * e.a4)) ofN 8
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


ha.ha
SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6 + -(e.a1 * e.a3 * e.a4) + 4 * e.a2 * e.a6) ofN 8
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


ha.hb
SurjVal.v evr.valtn (e.a2 * e.a3 * e.a3) ofN 8
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


ha
SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6 + -(e.a1 * e.a3 * e.a4) + 4 * e.a2 * e.a6 + e.a2 * e.a3 * e.a3) ofN 8
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


hb
SurjVal.v evr.valtn (-(e.a4 * e.a4)) ofN 8
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


ha.ha
SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6 + -(e.a1 * e.a3 * e.a4) + 4 * e.a2 * e.a6) ofN 8
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


ha.ha
SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6 + -(e.a1 * e.a3 * e.a4) + 4 * e.a2 * e.a6) ofN 8
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


ha.hb
SurjVal.v evr.valtn (e.a2 * e.a3 * e.a3) ofN 8
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


ha.ha.ha
SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6 + -(e.a1 * e.a3 * e.a4)) ofN 8
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


ha.ha.hb
SurjVal.v evr.valtn (4 * e.a2 * e.a6) ofN 8
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


ha.ha
SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6 + -(e.a1 * e.a3 * e.a4) + 4 * e.a2 * e.a6) ofN 8
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


ha.hb
SurjVal.v evr.valtn (e.a2 * e.a3 * e.a3) ofN 8
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


ha.ha.ha
SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6 + -(e.a1 * e.a3 * e.a4)) ofN 8
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


ha.ha.ha
SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6 + -(e.a1 * e.a3 * e.a4)) ofN 8
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


ha.ha.hb
SurjVal.v evr.valtn (4 * e.a2 * e.a6) ofN 8
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


ha.ha.ha.ha
SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6) ofN 8
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


ha.ha.ha.hb
SurjVal.v evr.valtn (-(e.a1 * e.a3 * e.a4)) ofN 8
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


ha.ha.ha
SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6 + -(e.a1 * e.a3 * e.a4)) ofN 8
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


ha.ha.hb
SurjVal.v evr.valtn (4 * e.a2 * e.a6) ofN 8
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


ha.ha.ha.ha
SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6) ofN 8
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


ha.ha.ha.ha
SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6) ofN 8
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


ha.ha.ha.hb
SurjVal.v evr.valtn (-(e.a1 * e.a3 * e.a4)) ofN 8

Goals accomplished! 🐙
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


ha.ha.ha
SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6 + -(e.a1 * e.a3 * e.a4)) ofN 8
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


ha.ha.hb
SurjVal.v evr.valtn (4 * e.a2 * e.a6) ofN 8
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


ha.ha.ha.hb
SurjVal.v evr.valtn (-(e.a1 * e.a3 * e.a4)) ofN 8
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


ha.ha.ha.hb
SurjVal.v evr.valtn (-(e.a1 * e.a3 * e.a4)) ofN 8
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


ha.ha.ha.hb
SurjVal.v evr.valtn (-(e.a1 * e.a3 * e.a4)) ofN 8
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


ha.ha.ha.hb
SurjVal.v evr.valtn (e.a1 * e.a3 * e.a4) ofN 8
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


ha.ha.ha.hb
SurjVal.v evr.valtn (e.a1 * e.a3 * e.a4) ofN 8
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


ha.ha.ha.hb
SurjVal.v evr.valtn (-(e.a1 * e.a3 * e.a4)) ofN 8

Goals accomplished! 🐙
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


ha.ha
SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6 + -(e.a1 * e.a3 * e.a4) + 4 * e.a2 * e.a6) ofN 8
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


ha.hb
SurjVal.v evr.valtn (e.a2 * e.a3 * e.a3) ofN 8
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


ha.ha.hb
SurjVal.v evr.valtn (4 * e.a2 * e.a6) ofN 8
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


ha.ha.hb
SurjVal.v evr.valtn (4 * e.a2 * e.a6) ofN 8
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


ha.ha.hb
SurjVal.v evr.valtn (4 * e.a2 * e.a6) ofN 8
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


ha.ha.hb
SurjVal.v evr.valtn (4 * (e.a2 * e.a6)) ofN 8
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


ha.ha.hb
SurjVal.v evr.valtn (4 * (e.a2 * e.a6)) ofN 8
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


ha.ha.hb
SurjVal.v evr.valtn (4 * e.a2 * e.a6) ofN 8

Goals accomplished! 🐙
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


ha
SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6 + -(e.a1 * e.a3 * e.a4) + 4 * e.a2 * e.a6 + e.a2 * e.a3 * e.a3) ofN 8
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


hb
SurjVal.v evr.valtn (-(e.a4 * e.a4)) ofN 8
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


ha.hb
SurjVal.v evr.valtn (e.a2 * e.a3 * e.a3) ofN 8
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


ha.hb
SurjVal.v evr.valtn (e.a2 * e.a3 * e.a3) ofN 8

Goals accomplished! 🐙
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


SurjVal.v evr.valtn (b8 e) ofN 8
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


hb
SurjVal.v evr.valtn (-(e.a4 * e.a4)) ofN 8
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


hb
SurjVal.v evr.valtn (-(e.a4 * e.a4)) ofN 8
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


hb
SurjVal.v evr.valtn (-(e.a4 * e.a4)) ofN 8
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


hb
SurjVal.v evr.valtn (e.a4 * e.a4) ofN 8
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


hb
SurjVal.v evr.valtn (e.a4 * e.a4) ofN 8
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


hb
SurjVal.v evr.valtn (-(e.a4 * e.a4)) ofN 8

Goals accomplished! 🐙
lemma
discr_of_pi_scaling: ∀ (evr : EnatValRing p) (e : Model R), SurjVal.v evr.valtn e.a1 ofN 1SurjVal.v evr.valtn e.a2 ofN 2SurjVal.v evr.valtn e.a3 ofN 3SurjVal.v evr.valtn e.a4 ofN 4SurjVal.v evr.valtn e.a6 ofN 6discr (pi_scaling evr e) = EnatValRing.sub_val evr (discr e) 12
discr_of_pi_scaling
(evr :
EnatValRing: {R : Type ?u.15809} → R[inst : IntegralDomain R] → Type ?u.15809
EnatValRing
p: R
p
) (
e: Model R
e
:
Model: (R : Type ?u.15817) → [inst : IntegralDomain R] → Type ?u.15817
Model
R: Type u
R
) (
h1: SurjVal.v evr.valtn e.a1 ofN 1
h1
: evr.
valtn: {R : Type ?u.15822} → {p : R} → [inst : IntegralDomain R] → EnatValRing pSurjVal p
valtn
.
v: {R : Type ?u.15829} → {p : R} → [inst : IntegralDomain R] → SurjVal pRℕ∪∞
v
e: Model R
e
.
a1: {R : Type ?u.15836} → [inst : IntegralDomain R] → Model RR
a1
ofN: ℕ∪∞
ofN
1: ?m.15842
1
) (
h2: SurjVal.v evr.valtn e.a2 ofN 2
h2
: evr.
valtn: {R : Type ?u.15860} → {p : R} → [inst : IntegralDomain R] → EnatValRing pSurjVal p
valtn
.
v: {R : Type ?u.15864} → {p : R} → [inst : IntegralDomain R] → SurjVal pRℕ∪∞
v
e: Model R
e
.
a2: {R : Type ?u.15868} → [inst : IntegralDomain R] → Model RR
a2
ofN: ℕ∪∞
ofN
2: ?m.15872
2
) (
h3: SurjVal.v evr.valtn e.a3 ofN 3
h3
: evr.
valtn: {R : Type ?u.15882} → {p : R} → [inst : IntegralDomain R] → EnatValRing pSurjVal p
valtn
.
v: {R : Type ?u.15886} → {p : R} → [inst : IntegralDomain R] → SurjVal pRℕ∪∞
v
e: Model R
e
.
a3: {R : Type ?u.15890} → [inst : IntegralDomain R] → Model RR
a3
ofN: ℕ∪∞
ofN
3: ?m.15894
3
) (
h4: SurjVal.v evr.valtn e.a4 ofN 4
h4
: evr.
valtn: {R : Type ?u.15904} → {p : R} → [inst : IntegralDomain R] → EnatValRing pSurjVal p
valtn
.
v: {R : Type ?u.15908} → {p : R} → [inst : IntegralDomain R] → SurjVal pRℕ∪∞
v
e: Model R
e
.
a4: {R : Type ?u.15912} → [inst : IntegralDomain R] → Model RR
a4
ofN: ℕ∪∞
ofN
4: ?m.15916
4
) (
h6: SurjVal.v evr.valtn e.a6 ofN 6
h6
: evr.
valtn: {R : Type ?u.15926} → {p : R} → [inst : IntegralDomain R] → EnatValRing pSurjVal p
valtn
.
v: {R : Type ?u.15930} → {p : R} → [inst : IntegralDomain R] → SurjVal pRℕ∪∞
v
e: Model R
e
.
a6: {R : Type ?u.15934} → [inst : IntegralDomain R] → Model RR
a6
ofN: ℕ∪∞
ofN
6: ?m.15938
6
) : (
pi_scaling: {R : Type ?u.15948} → [inst : IntegralDomain R] → {p : R} → EnatValRing pModel RModel R
pi_scaling
evr
e: Model R
e
).
discr: {R : Type ?u.15955} → [inst : IntegralDomain R] → Model RR
discr
= evr.
sub_val: {R : Type ?u.15961} → [inst : IntegralDomain R] → {p : R} → EnatValRing pRR
sub_val
e: Model R
e
.
discr: {R : Type ?u.15971} → [inst : IntegralDomain R] → Model RR
discr
12: ?m.15978
12
:=
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


-EnatValRing.sub_val evr (b2 e) 2 * EnatValRing.sub_val evr (b2 e) 2 * EnatValRing.sub_val evr (b8 e) 8 - 8 * EnatValRing.sub_val evr (b4 e) 4 ^ 3 - 27 * EnatValRing.sub_val evr (b6 e) 6 * EnatValRing.sub_val evr (b6 e) 6 + 9 * EnatValRing.sub_val evr (b2 e) 2 * EnatValRing.sub_val evr (b4 e) 4 * EnatValRing.sub_val evr (b6 e) 6 = EnatValRing.sub_val evr (-b2 e * b2 e * b8 e - 8 * b4 e ^ 3 - 27 * b6 e * b6 e + 9 * b2 e * b4 e * b6 e) 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6



Goals accomplished! 🐙
lemma
val_discr_of_val_ai: ∀ (evr : EnatValRing p) (e : Model R), SurjVal.v evr.valtn e.a1 ofN 1SurjVal.v evr.valtn e.a2 ofN 2SurjVal.v evr.valtn e.a3 ofN 3SurjVal.v evr.valtn e.a4 ofN 4SurjVal.v evr.valtn e.a6 ofN 6SurjVal.v evr.valtn (discr e) ofN 12
val_discr_of_val_ai
(evr :
EnatValRing: {R : Type ?u.16455} → R[inst : IntegralDomain R] → Type ?u.16455
EnatValRing
p: R
p
) (
e: Model R
e
:
Model: (R : Type ?u.16463) → [inst : IntegralDomain R] → Type ?u.16463
Model
R: Type u
R
) (
h1: SurjVal.v evr.valtn e.a1 ofN 1
h1
: evr.
valtn: {R : Type ?u.16468} → {p : R} → [inst : IntegralDomain R] → EnatValRing pSurjVal p
valtn
.
v: {R : Type ?u.16475} → {p : R} → [inst : IntegralDomain R] → SurjVal pRℕ∪∞
v
e: Model R
e
.
a1: {R : Type ?u.16482} → [inst : IntegralDomain R] → Model RR
a1
ofN: ℕ∪∞
ofN
1: ?m.16488
1
) (
h2: SurjVal.v evr.valtn e.a2 ofN 2
h2
: evr.
valtn: {R : Type ?u.16506} → {p : R} → [inst : IntegralDomain R] → EnatValRing pSurjVal p
valtn
.
v: {R : Type ?u.16510} → {p : R} → [inst : IntegralDomain R] → SurjVal pRℕ∪∞
v
e: Model R
e
.
a2: {R : Type ?u.16514} → [inst : IntegralDomain R] → Model RR
a2
ofN: ℕ∪∞
ofN
2: ?m.16518
2
) (
h3: SurjVal.v evr.valtn e.a3 ofN 3
h3
: evr.
valtn: {R : Type ?u.16528} → {p : R} → [inst : IntegralDomain R] → EnatValRing pSurjVal p
valtn
.
v: {R : Type ?u.16532} → {p : R} → [inst : IntegralDomain R] → SurjVal pRℕ∪∞
v
e: Model R
e
.
a3: {R : Type ?u.16536} → [inst : IntegralDomain R] → Model RR
a3
ofN: ℕ∪∞
ofN
3: ?m.16540
3
) (
h4: SurjVal.v evr.valtn e.a4 ofN 4
h4
: evr.
valtn: {R : Type ?u.16550} → {p : R} → [inst : IntegralDomain R] → EnatValRing pSurjVal p
valtn
.
v: {R : Type ?u.16554} → {p : R} → [inst : IntegralDomain R] → SurjVal pRℕ∪∞
v
e: Model R
e
.
a4: {R : Type ?u.16558} → [inst : IntegralDomain R] → Model RR
a4
ofN: ℕ∪∞
ofN
4: ?m.16562
4
) (
h6: SurjVal.v evr.valtn e.a6 ofN 6
h6
: evr.
valtn: {R : Type ?u.16572} → {p : R} → [inst : IntegralDomain R] → EnatValRing pSurjVal p
valtn
.
v: {R : Type ?u.16576} → {p : R} → [inst : IntegralDomain R] → SurjVal pRℕ∪∞
v
e: Model R
e
.
a6: {R : Type ?u.16580} → [inst : IntegralDomain R] → Model RR
a6
ofN: ℕ∪∞
ofN
6: ?m.16584
6
) : evr.
valtn: {R : Type ?u.16594} → {p : R} → [inst : IntegralDomain R] → EnatValRing pSurjVal p
valtn
.
v: {R : Type ?u.16598} → {p : R} → [inst : IntegralDomain R] → SurjVal pRℕ∪∞
v
e: Model R
e
.
discr: {R : Type ?u.16602} → [inst : IntegralDomain R] → Model RR
discr
ofN: ℕ∪∞
ofN
12: ?m.16609
12
:=
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


SurjVal.v evr.valtn (discr e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

hb2: SurjVal.v evr.valtn (b2 e) ofN 2


SurjVal.v evr.valtn (discr e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


SurjVal.v evr.valtn (discr e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4


SurjVal.v evr.valtn (discr e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


SurjVal.v evr.valtn (discr e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6


SurjVal.v evr.valtn (discr e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


SurjVal.v evr.valtn (discr e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


SurjVal.v evr.valtn (discr e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


SurjVal.v evr.valtn (discr e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


SurjVal.v evr.valtn (-b2 e * b2 e * b8 e + -(8 * b4 e ^ 3) + -(27 * b6 e * b6 e) + 9 * b2 e * b4 e * b6 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


SurjVal.v evr.valtn (discr e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


ha
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e + -(8 * b4 e ^ 3) + -(27 * b6 e * b6 e)) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hb
SurjVal.v evr.valtn (9 * b2 e * b4 e * b6 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


SurjVal.v evr.valtn (discr e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


ha
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e + -(8 * b4 e ^ 3) + -(27 * b6 e * b6 e)) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


ha
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e + -(8 * b4 e ^ 3) + -(27 * b6 e * b6 e)) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hb
SurjVal.v evr.valtn (9 * b2 e * b4 e * b6 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


ha.ha
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e + -(8 * b4 e ^ 3)) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


ha.hb
SurjVal.v evr.valtn (-(27 * b6 e * b6 e)) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


ha
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e + -(8 * b4 e ^ 3) + -(27 * b6 e * b6 e)) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hb
SurjVal.v evr.valtn (9 * b2 e * b4 e * b6 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


ha.ha
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e + -(8 * b4 e ^ 3)) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


ha.ha
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e + -(8 * b4 e ^ 3)) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


ha.hb
SurjVal.v evr.valtn (-(27 * b6 e * b6 e)) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


ha.ha.ha
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


ha.ha.hb
SurjVal.v evr.valtn (-(8 * b4 e ^ 3)) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


ha.ha
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e + -(8 * b4 e ^ 3)) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


ha.hb
SurjVal.v evr.valtn (-(27 * b6 e * b6 e)) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


ha.ha.ha
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


ha.ha.ha
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


ha.ha.hb
SurjVal.v evr.valtn (-(8 * b4 e ^ 3)) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


ha.ha.ha
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


ha.ha.ha
SurjVal.v evr.valtn (-(b2 e * b2 e) * b8 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


ha.ha.ha
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


ha.ha.ha
SurjVal.v evr.valtn (-(b2 e * b2 e * b8 e)) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


ha.ha.ha
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


ha.ha.ha
SurjVal.v evr.valtn (b2 e * b2 e * b8 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


ha.ha.ha
SurjVal.v evr.valtn (b2 e * b2 e * b8 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


ha.ha.ha
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


ha.ha.hb
SurjVal.v evr.valtn (-(8 * b4 e ^ 3)) ofN 12

Goals accomplished! 🐙
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


ha.ha
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e + -(8 * b4 e ^ 3)) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


ha.hb
SurjVal.v evr.valtn (-(27 * b6 e * b6 e)) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


ha.ha.hb
SurjVal.v evr.valtn (-(8 * b4 e ^ 3)) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


ha.ha.hb
SurjVal.v evr.valtn (-(8 * b4 e ^ 3)) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


ha.ha.hb
SurjVal.v evr.valtn (-(8 * b4 e ^ 3)) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


ha.ha.hb
SurjVal.v evr.valtn (8 * b4 e ^ 3) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


ha.ha.hb
SurjVal.v evr.valtn (-(8 * b4 e ^ 3)) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


ha.ha.hb
SurjVal.v evr.valtn (8 * (b4 e ^ 2 * b4 e)) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


ha.ha.hb
SurjVal.v evr.valtn (-(8 * b4 e ^ 3)) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


ha.ha.hb
SurjVal.v evr.valtn (8 * (b4 e ^ 1 * b4 e * b4 e)) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


ha.ha.hb
SurjVal.v evr.valtn (-(8 * b4 e ^ 3)) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


ha.ha.hb
SurjVal.v evr.valtn (8 * (b4 e * b4 e * b4 e)) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


ha.ha.hb
SurjVal.v evr.valtn (8 * (b4 e * b4 e * b4 e)) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


ha.ha.hb
SurjVal.v evr.valtn (-(8 * b4 e ^ 3)) ofN 12

Goals accomplished! 🐙
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


ha
SurjVal.v evr.valtn (-b2 e * b2 e * b8 e + -(8 * b4 e ^ 3) + -(27 * b6 e * b6 e)) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hb
SurjVal.v evr.valtn (9 * b2 e * b4 e * b6 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


ha.hb
SurjVal.v evr.valtn (-(27 * b6 e * b6 e)) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


ha.hb
SurjVal.v evr.valtn (-(27 * b6 e * b6 e)) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


ha.hb
SurjVal.v evr.valtn (-(27 * b6 e * b6 e)) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


ha.hb
SurjVal.v evr.valtn (27 * b6 e * b6 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


ha.hb
SurjVal.v evr.valtn (-(27 * b6 e * b6 e)) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


ha.hb
SurjVal.v evr.valtn (27 * (b6 e * b6 e)) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


ha.hb
SurjVal.v evr.valtn (27 * (b6 e * b6 e)) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


ha.hb
SurjVal.v evr.valtn (-(27 * b6 e * b6 e)) ofN 12

Goals accomplished! 🐙
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6


SurjVal.v evr.valtn (discr e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hb
SurjVal.v evr.valtn (9 * b2 e * b4 e * b6 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hb
SurjVal.v evr.valtn (9 * b2 e * b4 e * b6 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hb
SurjVal.v evr.valtn (9 * b2 e * b4 e * b6 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hb
SurjVal.v evr.valtn (9 * b2 e * (b4 e * b6 e)) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hb
SurjVal.v evr.valtn (9 * b2 e * b4 e * b6 e) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hb
SurjVal.v evr.valtn (9 * (b2 e * (b4 e * b6 e))) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hb
SurjVal.v evr.valtn (9 * (b2 e * (b4 e * b6 e))) ofN 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: Model R

h1: SurjVal.v evr.valtn e.a1 ofN 1

h2: SurjVal.v evr.valtn e.a2 ofN 2

h3: SurjVal.v evr.valtn e.a3 ofN 3

h4: SurjVal.v evr.valtn e.a4 ofN 4

h6: SurjVal.v evr.valtn e.a6 ofN 6

hb2: SurjVal.v evr.valtn (b2 e) ofN 2

hb4: SurjVal.v evr.valtn (b4 e) ofN 4

hb6: SurjVal.v evr.valtn (b6 e) ofN 6

hb8: SurjVal.v evr.valtn (b8 e) ofN 8


hb
SurjVal.v evr.valtn (9 * b2 e * b4 e * b6 e) ofN 12

Goals accomplished! 🐙
end Model namespace ValidModel def
pi_scaling: {p : R} → (evr : EnatValRing p) → (e : ValidModel R) → SurjVal.v evr.valtn e.toModel.a1 ofN 1SurjVal.v evr.valtn e.toModel.a2 ofN 2SurjVal.v evr.valtn e.toModel.a3 ofN 3SurjVal.v evr.valtn e.toModel.a4 ofN 4SurjVal.v evr.valtn e.toModel.a6 ofN 6ValidModel R
pi_scaling
(evr :
EnatValRing: {R : Type ?u.18015} → R[inst : IntegralDomain R] → Type ?u.18015
EnatValRing
p: ?m.18012
p
) (e :
ValidModel: (R : Type ?u.18022) → [inst : IntegralDomain R] → Type ?u.18022
ValidModel
R: Type u
R
) (
h1: SurjVal.v evr.valtn e.toModel.a1 ofN 1
h1
: evr.
valtn: {R : Type ?u.18030} → {p : R} → [inst : IntegralDomain R] → EnatValRing pSurjVal p
valtn
.
v: {R : Type ?u.18042} → {p : R} → [inst : IntegralDomain R] → SurjVal pRℕ∪∞
v
e.
a1: {R : Type ?u.18057} → [inst : IntegralDomain R] → Model RR
a1
ofN: ℕ∪∞
ofN
1: ?m.18063
1
) (
h2: SurjVal.v evr.valtn e.toModel.a2 ofN 2
h2
: evr.
valtn: {R : Type ?u.18081} → {p : R} → [inst : IntegralDomain R] → EnatValRing pSurjVal p
valtn
.
v: {R : Type ?u.18088} → {p : R} → [inst : IntegralDomain R] → SurjVal pRℕ∪∞
v
e.
a2: {R : Type ?u.18098} → [inst : IntegralDomain R] → Model RR
a2
ofN: ℕ∪∞
ofN
2: ?m.18102
2
) (
h3: SurjVal.v evr.valtn e.toModel.a3 ofN 3
h3
: evr.
valtn: {R : Type ?u.18112} → {p : R} → [inst : IntegralDomain R] → EnatValRing pSurjVal p
valtn
.
v: {R : Type ?u.18116} → {p : R} → [inst : IntegralDomain R] → SurjVal pRℕ∪∞
v
e.
a3: {R : Type ?u.18123} → [inst : IntegralDomain R] → Model RR
a3
ofN: ℕ∪∞
ofN
3: ?m.18127
3
) (
h4: SurjVal.v evr.valtn e.toModel.a4 ofN 4
h4
: evr.
valtn: {R : Type ?u.18137} → {p : R} → [inst : IntegralDomain R] → EnatValRing pSurjVal p
valtn
.
v: {R : Type ?u.18141} → {p : R} → [inst : IntegralDomain R] → SurjVal pRℕ∪∞
v
e.
a4: {R : Type ?u.18148} → [inst : IntegralDomain R] → Model RR
a4
ofN: ℕ∪∞
ofN
4: ?m.18152
4
) (
h6: SurjVal.v evr.valtn e.toModel.a6 ofN 6
h6
: evr.
valtn: {R : Type ?u.18162} → {p : R} → [inst : IntegralDomain R] → EnatValRing pSurjVal p
valtn
.
v: {R : Type ?u.18166} → {p : R} → [inst : IntegralDomain R] → SurjVal pRℕ∪∞
v
e.
a6: {R : Type ?u.18173} → [inst : IntegralDomain R] → Model RR
a6
ofN: ℕ∪∞
ofN
6: ?m.18177
6
) :
ValidModel: (R : Type ?u.18186) → [inst : IntegralDomain R] → Type ?u.18186
ValidModel
R: Type u
R
:= { toModel :=
Model.pi_scaling: {R : Type ?u.18200} → [inst : IntegralDomain R] → {p : R} → EnatValRing pModel RModel R
Model.pi_scaling
evr e.
toModel: {R : Type ?u.18204} → [inst : IntegralDomain R] → ValidModel RModel R
toModel
, discr_not_zero :=
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: ValidModel R

h1: SurjVal.v evr.valtn e.toModel.a1 ofN 1

h2: SurjVal.v evr.valtn e.toModel.a2 ofN 2

h3: SurjVal.v evr.valtn e.toModel.a3 ofN 3

h4: SurjVal.v evr.valtn e.toModel.a4 ofN 4

h6: SurjVal.v evr.valtn e.toModel.a6 ofN 6


Model.discr (Model.pi_scaling evr e.toModel) 0
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: ValidModel R

h1: SurjVal.v evr.valtn e.toModel.a1 ofN 1

h2: SurjVal.v evr.valtn e.toModel.a2 ofN 2

h3: SurjVal.v evr.valtn e.toModel.a3 ofN 3

h4: SurjVal.v evr.valtn e.toModel.a4 ofN 4

h6: SurjVal.v evr.valtn e.toModel.a6 ofN 6


Model.discr (Model.pi_scaling evr e.toModel) 0
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: ValidModel R

h1: SurjVal.v evr.valtn e.toModel.a1 ofN 1

h2: SurjVal.v evr.valtn e.toModel.a2 ofN 2

h3: SurjVal.v evr.valtn e.toModel.a3 ofN 3

h4: SurjVal.v evr.valtn e.toModel.a4 ofN 4

h6: SurjVal.v evr.valtn e.toModel.a6 ofN 6


EnatValRing.sub_val evr (Model.discr e.toModel) 12 0
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: ValidModel R

h1: SurjVal.v evr.valtn e.toModel.a1 ofN 1

h2: SurjVal.v evr.valtn e.toModel.a2 ofN 2

h3: SurjVal.v evr.valtn e.toModel.a3 ofN 3

h4: SurjVal.v evr.valtn e.toModel.a4 ofN 4

h6: SurjVal.v evr.valtn e.toModel.a6 ofN 6


EnatValRing.sub_val evr (Model.discr e.toModel) 12 0
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: ValidModel R

h1: SurjVal.v evr.valtn e.toModel.a1 ofN 1

h2: SurjVal.v evr.valtn e.toModel.a2 ofN 2

h3: SurjVal.v evr.valtn e.toModel.a3 ofN 3

h4: SurjVal.v evr.valtn e.toModel.a4 ofN 4

h6: SurjVal.v evr.valtn e.toModel.a6 ofN 6


Model.discr (Model.pi_scaling evr e.toModel) 0
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: ValidModel R

h1: SurjVal.v evr.valtn e.toModel.a1 ofN 1

h2: SurjVal.v evr.valtn e.toModel.a2 ofN 2

h3: SurjVal.v evr.valtn e.toModel.a3 ofN 3

h4: SurjVal.v evr.valtn e.toModel.a4 ofN 4

h6: SurjVal.v evr.valtn e.toModel.a6 ofN 6

H: EnatValRing.sub_val evr (Model.discr e.toModel) 12 = 0


R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: ValidModel R

h1: SurjVal.v evr.valtn e.toModel.a1 ofN 1

h2: SurjVal.v evr.valtn e.toModel.a2 ofN 2

h3: SurjVal.v evr.valtn e.toModel.a3 ofN 3

h4: SurjVal.v evr.valtn e.toModel.a4 ofN 4

h6: SurjVal.v evr.valtn e.toModel.a6 ofN 6


Model.discr (Model.pi_scaling evr e.toModel) 0
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: ValidModel R

h1: SurjVal.v evr.valtn e.toModel.a1 ofN 1

h2: SurjVal.v evr.valtn e.toModel.a2 ofN 2

h3: SurjVal.v evr.valtn e.toModel.a3 ofN 3

h4: SurjVal.v evr.valtn e.toModel.a4 ofN 4

h6: SurjVal.v evr.valtn e.toModel.a6 ofN 6

H: EnatValRing.sub_val evr (Model.discr e.toModel) 12 = 0

H': (let x := EnatValRing.sub_val evr (Model.discr e.toModel) 12; (fun x => p ^ 12 * x) x) = let x := 0; (fun x => p ^ 12 * x) x


R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: ValidModel R

h1: SurjVal.v evr.valtn e.toModel.a1 ofN 1

h2: SurjVal.v evr.valtn e.toModel.a2 ofN 2

h3: SurjVal.v evr.valtn e.toModel.a3 ofN 3

h4: SurjVal.v evr.valtn e.toModel.a4 ofN 4

h6: SurjVal.v evr.valtn e.toModel.a6 ofN 6


Model.discr (Model.pi_scaling evr e.toModel) 0
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: ValidModel R

h1: SurjVal.v evr.valtn e.toModel.a1 ofN 1

h2: SurjVal.v evr.valtn e.toModel.a2 ofN 2

h3: SurjVal.v evr.valtn e.toModel.a3 ofN 3

h4: SurjVal.v evr.valtn e.toModel.a4 ofN 4

h6: SurjVal.v evr.valtn e.toModel.a6 ofN 6

H: EnatValRing.sub_val evr (Model.discr e.toModel) 12 = 0

H': p ^ 12 * EnatValRing.sub_val evr (Model.discr e.toModel) 12 = 0


R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: ValidModel R

h1: SurjVal.v evr.valtn e.toModel.a1 ofN 1

h2: SurjVal.v evr.valtn e.toModel.a2 ofN 2

h3: SurjVal.v evr.valtn e.toModel.a3 ofN 3

h4: SurjVal.v evr.valtn e.toModel.a4 ofN 4

h6: SurjVal.v evr.valtn e.toModel.a6 ofN 6


Model.discr (Model.pi_scaling evr e.toModel) 0
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: ValidModel R

h1: SurjVal.v evr.valtn e.toModel.a1 ofN 1

h2: SurjVal.v evr.valtn e.toModel.a2 ofN 2

h3: SurjVal.v evr.valtn e.toModel.a3 ofN 3

h4: SurjVal.v evr.valtn e.toModel.a4 ofN 4

h6: SurjVal.v evr.valtn e.toModel.a6 ofN 6

H: EnatValRing.sub_val evr (Model.discr e.toModel) 12 = 0

H': p ^ 12 * EnatValRing.sub_val evr (Model.discr e.toModel) 12 = 0


R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: ValidModel R

h1: SurjVal.v evr.valtn e.toModel.a1 ofN 1

h2: SurjVal.v evr.valtn e.toModel.a2 ofN 2

h3: SurjVal.v evr.valtn e.toModel.a3 ofN 3

h4: SurjVal.v evr.valtn e.toModel.a4 ofN 4

h6: SurjVal.v evr.valtn e.toModel.a6 ofN 6

H: EnatValRing.sub_val evr (Model.discr e.toModel) 12 = 0

H': Model.discr e.toModel = 0


R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: ValidModel R

h1: SurjVal.v evr.valtn e.toModel.a1 ofN 1

h2: SurjVal.v evr.valtn e.toModel.a2 ofN 2

h3: SurjVal.v evr.valtn e.toModel.a3 ofN 3

h4: SurjVal.v evr.valtn e.toModel.a4 ofN 4

h6: SurjVal.v evr.valtn e.toModel.a6 ofN 6

H: EnatValRing.sub_val evr (Model.discr e.toModel) 12 = 0

H': Model.discr e.toModel = 0


R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: ValidModel R

h1: SurjVal.v evr.valtn e.toModel.a1 ofN 1

h2: SurjVal.v evr.valtn e.toModel.a2 ofN 2

h3: SurjVal.v evr.valtn e.toModel.a3 ofN 3

h4: SurjVal.v evr.valtn e.toModel.a4 ofN 4

h6: SurjVal.v evr.valtn e.toModel.a6 ofN 6

H: EnatValRing.sub_val evr (Model.discr e.toModel) 12 = 0

H': Model.discr e.toModel = 0


R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: ValidModel R

h1: SurjVal.v evr.valtn e.toModel.a1 ofN 1

h2: SurjVal.v evr.valtn e.toModel.a2 ofN 2

h3: SurjVal.v evr.valtn e.toModel.a3 ofN 3

h4: SurjVal.v evr.valtn e.toModel.a4 ofN 4

h6: SurjVal.v evr.valtn e.toModel.a6 ofN 6


Model.discr (Model.pi_scaling evr e.toModel) 0

Goals accomplished! 🐙
} lemma
toModel_pi_scaling: ∀ {R : Type u} [inst : IntegralDomain R] {p : R} (evr : EnatValRing p) (e : ValidModel R) (h1 : SurjVal.v evr.valtn e.toModel.a1 ofN 1) (h2 : SurjVal.v evr.valtn e.toModel.a2 ofN 2) (h3 : SurjVal.v evr.valtn e.toModel.a3 ofN 3) (h4 : SurjVal.v evr.valtn e.toModel.a4 ofN 4) (h6 : SurjVal.v evr.valtn e.toModel.a6 ofN 6), (pi_scaling evr e h1 h2 h3 h4 h6).toModel = Model.pi_scaling evr e.toModel
toModel_pi_scaling
(evr :
EnatValRing: {R : Type ?u.18940} → R[inst : IntegralDomain R] → Type ?u.18940
EnatValRing
p: ?m.18937
p
) (e :
ValidModel: (R : Type ?u.18947) → [inst : IntegralDomain R] → Type ?u.18947
ValidModel
R: Type u
R
) (
h1: SurjVal.v evr.valtn e.toModel.a1 ofN 1
h1
: evr.
valtn: {R : Type ?u.18955} → {p : R} → [inst : IntegralDomain R] → EnatValRing pSurjVal p
valtn
.
v: {R : Type ?u.18967} → {p : R} → [inst : IntegralDomain R] → SurjVal pRℕ∪∞
v
e.
a1: {R : Type ?u.18982} → [inst : IntegralDomain R] → Model RR
a1
ofN: ℕ∪∞
ofN
1: ?m.18988
1
) (
h2: SurjVal.v evr.valtn e.toModel.a2 ofN 2
h2
: evr.
valtn: {R : Type ?u.19006} → {p : R} → [inst : IntegralDomain R] → EnatValRing pSurjVal p
valtn
.
v: {R : Type ?u.19013} → {p : R} → [inst : IntegralDomain R] → SurjVal pRℕ∪∞
v
e.
a2: {R : Type ?u.19023} → [inst : IntegralDomain R] → Model RR
a2
ofN: ℕ∪∞
ofN
2: ?m.19027
2
) (
h3: SurjVal.v evr.valtn e.toModel.a3 ofN 3
h3
: evr.
valtn: {R : Type ?u.19037} → {p : R} → [inst : IntegralDomain R] → EnatValRing pSurjVal p
valtn
.
v: {R : Type ?u.19041} → {p : R} → [inst : IntegralDomain R] → SurjVal pRℕ∪∞
v
e.
a3: {R : Type ?u.19048} → [inst : IntegralDomain R] → Model RR
a3
ofN: ℕ∪∞
ofN
3: ?m.19052
3
) (
h4: SurjVal.v evr.valtn e.toModel.a4 ofN 4
h4
: evr.
valtn: {R : Type ?u.19062} → {p : R} → [inst : IntegralDomain R] → EnatValRing pSurjVal p
valtn
.
v: {R : Type ?u.19066} → {p : R} → [inst : IntegralDomain R] → SurjVal pRℕ∪∞
v
e.
a4: {R : Type ?u.19073} → [inst : IntegralDomain R] → Model RR
a4
ofN: ℕ∪∞
ofN
4: ?m.19077
4
) (
h6: SurjVal.v evr.valtn e.toModel.a6 ofN 6
h6
: evr.
valtn: {R : Type ?u.19087} → {p : R} → [inst : IntegralDomain R] → EnatValRing pSurjVal p
valtn
.
v: {R : Type ?u.19091} → {p : R} → [inst : IntegralDomain R] → SurjVal pRℕ∪∞
v
e.
a6: {R : Type ?u.19098} → [inst : IntegralDomain R] → Model RR
a6
ofN: ℕ∪∞
ofN
6: ?m.19102
6
) : (e.
pi_scaling: {R : Type ?u.19112} → [inst : IntegralDomain R] → {p : R} → (evr : EnatValRing p) → (e : ValidModel R) → SurjVal.v evr.valtn e.toModel.a1 ofN 1SurjVal.v evr.valtn e.toModel.a2 ofN 2SurjVal.v evr.valtn e.toModel.a3 ofN 3SurjVal.v evr.valtn e.toModel.a4 ofN 4SurjVal.v evr.valtn e.toModel.a6 ofN 6ValidModel R
pi_scaling
evr
h1: SurjVal.v evr.valtn e.toModel.a1 ofN 1
h1
h2: SurjVal.v evr.valtn e.toModel.a2 ofN 2
h2
h3: SurjVal.v evr.valtn e.toModel.a3 ofN 3
h3
h4: SurjVal.v evr.valtn e.toModel.a4 ofN 4
h4
h6: SurjVal.v evr.valtn e.toModel.a6 ofN 6
h6
).
toModel: {R : Type ?u.19133} → [inst : IntegralDomain R] → ValidModel RModel R
toModel
= e.
toModel: {R : Type ?u.19136} → [inst : IntegralDomain R] → ValidModel RModel R
toModel
.
pi_scaling: {R : Type ?u.19139} → [inst : IntegralDomain R] → {p : R} → EnatValRing pModel RModel R
pi_scaling
evr :=
rfl: ∀ {α : Sort ?u.19161} {a : α}, a = a
rfl
def
val_discr_to_nat: {p : R} → SurjVal pValidModel R
val_discr_to_nat
{
p: R
p
:
R: Type u
R
} (
valp: SurjVal p
valp
:
SurjVal: {R : Type ?u.19353} → R[inst : IntegralDomain R] → Type ?u.19353
SurjVal
p: R
p
) (e :
ValidModel: (R : Type ?u.19361) → [inst : IntegralDomain R] → Type ?u.19361
ValidModel
R: Type u
R
) :
: Type
:=
nat_of_val: {R : Type ?u.19369} → [inst : IntegralDomain R] → {p : R} → SurjVal p{a : R} → a 0
nat_of_val
valp: SurjVal p
valp
e.
discr_not_zero: ∀ {R : Type ?u.19380} [inst : IntegralDomain R] (self : ValidModel R), Model.discr self.toModel 0
discr_not_zero
@[simp] lemma
iso_rst_val_discr_to_nat: ∀ {p : R} (valp : SurjVal p) (r s t : R) (e : ValidModel R), val_discr_to_nat valp (rst_iso r s t e) = val_discr_to_nat valp e
iso_rst_val_discr_to_nat
{
p: R
p
:
R: Type u
R
} (
valp: SurjVal p
valp
:
SurjVal: {R : Type ?u.19441} → R[inst : IntegralDomain R] → Type ?u.19441
SurjVal
p: R
p
) (
r: R
r
s: R
s
t: R
t
:
R: Type u
R
) (e :
ValidModel: (R : Type ?u.19455) → [inst : IntegralDomain R] → Type ?u.19455
ValidModel
R: Type u
R
) :
val_discr_to_nat: {R : Type ?u.19460} → [inst : IntegralDomain R] → {p : R} → SurjVal pValidModel R
val_discr_to_nat
valp: SurjVal p
valp
(
rst_iso: {R : Type ?u.19470} → [inst : IntegralDomain R] → RRRValidModel RValidModel R
rst_iso
r: R
r
s: R
s
t: R
t
e) =
val_discr_to_nat: {R : Type ?u.19475} → [inst : IntegralDomain R] → {p : R} → SurjVal pValidModel R
val_discr_to_nat
valp: SurjVal p
valp
e :=
R: Type u

inst: IntegralDomain R

p: R

valp: SurjVal p

r, s, t: R

e: ValidModel R



Goals accomplished! 🐙
lemma
ofN_val_discr_to_nat: ∀ {p : R} (valp : SurjVal p) (e : ValidModel R), ofN (val_discr_to_nat valp e) = SurjVal.v valp (Model.discr e.toModel)
ofN_val_discr_to_nat
{
p: R
p
:
R: Type u
R
} (
valp: SurjVal p
valp
:
SurjVal: {R : Type ?u.19877} → R[inst : IntegralDomain R] → Type ?u.19877
SurjVal
p: R
p
) (e :
ValidModel: (R : Type ?u.19885) → [inst : IntegralDomain R] → Type ?u.19885
ValidModel
R: Type u
R
) :
ofN: ℕ∪∞
ofN
(
val_discr_to_nat: {R : Type ?u.19890} → [inst : IntegralDomain R] → {p : R} → SurjVal pValidModel R
val_discr_to_nat
valp: SurjVal p
valp
e) =
valp: SurjVal p
valp
.
v: {R : Type ?u.19902} → {p : R} → [inst : IntegralDomain R] → SurjVal pRℕ∪∞
v
e.
discr: {R : Type ?u.19909} → [inst : IntegralDomain R] → Model RR
discr
:=
R: Type u

inst: IntegralDomain R

p: R

valp: SurjVal p

e: ValidModel R


ofN (val_discr_to_nat valp e) = SurjVal.v valp (Model.discr e.toModel)
R: Type u

inst: IntegralDomain R

p: R

valp: SurjVal p

e: ValidModel R

x✝: ℕ∪∞

h: SurjVal.v valp (Model.discr e.toModel) = x✝


ofN (val_discr_to_nat valp e) = x✝
R: Type u

inst: IntegralDomain R

p: R

valp: SurjVal p

e: ValidModel R

n:

h: SurjVal.v valp (Model.discr e.toModel) = ofN n


ofN
R: Type u

inst: IntegralDomain R

p: R

valp: SurjVal p

e: ValidModel R

n:

h: SurjVal.v valp (Model.discr e.toModel) = ofN n


ofN
R: Type u

inst: IntegralDomain R

p: R

valp: SurjVal p

e: ValidModel R

n:

h: SurjVal.v valp (Model.discr e.toModel) = ofN n


ofN
ofN (nat_of_val valp (_ : Model.discr e.toModel 0)) = ofN n
R: Type u

inst: IntegralDomain R

p: R

valp: SurjVal p

e: ValidModel R

n:

h: SurjVal.v valp (Model.discr e.toModel) = ofN n


ofN
R: Type u

inst: IntegralDomain R

p: R

valp: SurjVal p

e: ValidModel R

n:

h: SurjVal.v valp (Model.discr e.toModel) = ofN n


ofN
ofN (to_nat (_ : ¬SurjVal.v valp (Model.discr e.toModel) = )) = ofN n
R: Type u

inst: IntegralDomain R

p: R

valp: SurjVal p

e: ValidModel R

n:

h: SurjVal.v valp (Model.discr e.toModel) = ofN n


ofN
R: Type u

inst: IntegralDomain R

p: R

valp: SurjVal p

e: ValidModel R

n:

h: SurjVal.v valp (Model.discr e.toModel) = ofN n


ofN
SurjVal.v valp (Model.discr e.toModel) = ofN n
R: Type u

inst: IntegralDomain R

p: R

valp: SurjVal p

e: ValidModel R

n:

h: SurjVal.v valp (Model.discr e.toModel) = ofN n


ofN
SurjVal.v valp (Model.discr e.toModel) = ofN n
R: Type u

inst: IntegralDomain R

p: R

valp: SurjVal p

e: ValidModel R

n:

h: SurjVal.v valp (Model.discr e.toModel) = ofN n


ofN

Goals accomplished! 🐙
R: Type u

inst: IntegralDomain R

p: R

valp: SurjVal p

e: ValidModel R

x✝: ℕ∪∞

h: SurjVal.v valp (Model.discr e.toModel) = x✝


ofN (val_discr_to_nat valp e) = x✝
R: Type u

inst: IntegralDomain R

p: R

valp: SurjVal p

e: ValidModel R

h: SurjVal.v valp (Model.discr e.toModel) =


top
R: Type u

inst: IntegralDomain R

p: R

valp: SurjVal p

e: ValidModel R

h: SurjVal.v valp (Model.discr e.toModel) =


top.h
R: Type u

inst: IntegralDomain R

p: R

valp: SurjVal p

e: ValidModel R

h: SurjVal.v valp (Model.discr e.toModel) =


top
R: Type u

inst: IntegralDomain R

p: R

valp: SurjVal p

e: ValidModel R

h: SurjVal.v valp (Model.discr e.toModel) =


top.h
R: Type u

inst: IntegralDomain R

p: R

valp: SurjVal p

e: ValidModel R

h: Model.discr e.toModel = 0


top.h
R: Type u

inst: IntegralDomain R

p: R

valp: SurjVal p

e: ValidModel R

h: Model.discr e.toModel = 0


top.h
R: Type u

inst: IntegralDomain R

p: R

valp: SurjVal p

e: ValidModel R

h: Model.discr e.toModel = 0


top.h
R: Type u

inst: IntegralDomain R

p: R

valp: SurjVal p

e: ValidModel R

h: SurjVal.v valp (Model.discr e.toModel) =


top

Goals accomplished! 🐙
lemma
pi_scaling_val_discr_to_nat: ∀ {p : R} (evr : EnatValRing p) (e : ValidModel R) (h1 : SurjVal.v evr.valtn e.toModel.a1 ofN 1) (h2 : SurjVal.v evr.valtn e.toModel.a2 ofN 2) (h3 : SurjVal.v evr.valtn e.toModel.a3 ofN 3) (h4 : SurjVal.v evr.valtn e.toModel.a4 ofN 4) (h6 : SurjVal.v evr.valtn e.toModel.a6 ofN 6), val_discr_to_nat evr.valtn (pi_scaling evr e h1 h2 h3 h4 h6) = val_discr_to_nat evr.valtn e - 12
pi_scaling_val_discr_to_nat
{
p: R
p
:
R: Type u
R
} (evr :
EnatValRing: {R : Type ?u.20155} → R[inst : IntegralDomain R] → Type ?u.20155
EnatValRing
p: R
p
) (e :
ValidModel: (R : Type ?u.20163) → [inst : IntegralDomain R] → Type ?u.20163
ValidModel
R: Type u
R
) (
h1: SurjVal.v evr.valtn e.toModel.a1 ofN 1
h1
: evr.
valtn: {R : Type ?u.20168} → {p : R} → [inst : IntegralDomain R] → EnatValRing pSurjVal p
valtn
.
v: {R : Type ?u.20175} → {p : R} → [inst : IntegralDomain R] → SurjVal pRℕ∪∞
v
e.
a1: {R : Type ?u.20187} → [inst : IntegralDomain R] → Model RR
a1
ofN: ℕ∪∞
ofN
1: ?m.20193
1
) (
h2: SurjVal.v evr.valtn e.toModel.a2 ofN 2
h2
: evr.
valtn: {R : Type ?u.20211} → {p : R} → [inst : IntegralDomain R] → EnatValRing pSurjVal p
valtn
.
v: {R : Type ?u.20215} → {p : R} → [inst : IntegralDomain R] → SurjVal pRℕ∪∞
v
e.
a2: {R : Type ?u.20222} → [inst : IntegralDomain R] → Model RR
a2
ofN: ℕ∪∞
ofN
2: ?m.20226
2
) (
h3: SurjVal.v evr.valtn e.toModel.a3 ofN 3
h3
: evr.
valtn: {R : Type ?u.20236} → {p : R} → [inst : IntegralDomain R] → EnatValRing pSurjVal p
valtn
.
v: {R : Type ?u.20240} → {p : R} → [inst : IntegralDomain R] → SurjVal pRℕ∪∞
v
e.
a3: {R : Type ?u.20247} → [inst : IntegralDomain R] → Model RR
a3
ofN: ℕ∪∞
ofN
3: ?m.20251
3
) (
h4: SurjVal.v evr.valtn e.toModel.a4 ofN 4
h4
: evr.
valtn: {R : Type ?u.20261} → {p : R} → [inst : IntegralDomain R] → EnatValRing pSurjVal p
valtn
.
v: {R : Type ?u.20265} → {p : R} → [inst : IntegralDomain R] → SurjVal pRℕ∪∞
v
e.
a4: {R : Type ?u.20272} → [inst : IntegralDomain R] → Model RR
a4
ofN: ℕ∪∞
ofN
4: ?m.20276
4
) (
h6: SurjVal.v evr.valtn e.toModel.a6 ofN 6
h6
: evr.
valtn: {R : Type ?u.20286} → {p : R} → [inst : IntegralDomain R] → EnatValRing pSurjVal p
valtn
.
v: {R : Type ?u.20290} → {p : R} → [inst : IntegralDomain R] → SurjVal pRℕ∪∞
v
e.
a6: {R : Type ?u.20297} → [inst : IntegralDomain R] → Model RR
a6
ofN: ℕ∪∞
ofN
6: ?m.20301
6
) :
val_discr_to_nat: {R : Type ?u.20311} → [inst : IntegralDomain R] → {p : R} → SurjVal pValidModel R
val_discr_to_nat
evr.
valtn: {R : Type ?u.20315} → {p : R} → [inst : IntegralDomain R] → EnatValRing pSurjVal p
valtn
(
pi_scaling: {R : Type ?u.20322} → [inst : IntegralDomain R] → {p : R} → (evr : EnatValRing p) → (e : ValidModel R) → SurjVal.v evr.valtn e.toModel.a1 ofN 1SurjVal.v evr.valtn e.toModel.a2 ofN 2SurjVal.v evr.valtn e.toModel.a3 ofN 3SurjVal.v evr.valtn e.toModel.a4 ofN 4SurjVal.v evr.valtn e.toModel.a6 ofN 6ValidModel R
pi_scaling
evr e
h1: SurjVal.v evr.valtn e.toModel.a1 ofN 1
h1
h2: SurjVal.v evr.valtn e.toModel.a2 ofN 2
h2
h3: SurjVal.v evr.valtn e.toModel.a3 ofN 3
h3
h4: SurjVal.v evr.valtn e.toModel.a4 ofN 4
h4
h6: SurjVal.v evr.valtn e.toModel.a6 ofN 6
h6
) =
val_discr_to_nat: {R : Type ?u.20333} → [inst : IntegralDomain R] → {p : R} → SurjVal pValidModel R
val_discr_to_nat
evr.
valtn: {R : Type ?u.20337} → {p : R} → [inst : IntegralDomain R] → EnatValRing pSurjVal p
valtn
e -
12: ?m.20345
12
:=
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: ValidModel R

h1: SurjVal.v evr.valtn e.toModel.a1 ofN 1

h2: SurjVal.v evr.valtn e.toModel.a2 ofN 2

h3: SurjVal.v evr.valtn e.toModel.a3 ofN 3

h4: SurjVal.v evr.valtn e.toModel.a4 ofN 4

h6: SurjVal.v evr.valtn e.toModel.a6 ofN 6


val_discr_to_nat evr.valtn (pi_scaling evr e h1 h2 h3 h4 h6) = val_discr_to_nat evr.valtn e - 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: ValidModel R

h1: SurjVal.v evr.valtn e.toModel.a1 ofN 1

h2: SurjVal.v evr.valtn e.toModel.a2 ofN 2

h3: SurjVal.v evr.valtn e.toModel.a3 ofN 3

h4: SurjVal.v evr.valtn e.toModel.a4 ofN 4

h6: SurjVal.v evr.valtn e.toModel.a6 ofN 6


val_discr_to_nat evr.valtn (pi_scaling evr e h1 h2 h3 h4 h6) = val_discr_to_nat evr.valtn e - 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: ValidModel R

h1: SurjVal.v evr.valtn e.toModel.a1 ofN 1

h2: SurjVal.v evr.valtn e.toModel.a2 ofN 2

h3: SurjVal.v evr.valtn e.toModel.a3 ofN 3

h4: SurjVal.v evr.valtn e.toModel.a4 ofN 4

h6: SurjVal.v evr.valtn e.toModel.a6 ofN 6


ofN (val_discr_to_nat evr.valtn (pi_scaling evr e h1 h2 h3 h4 h6)) = ofN (val_discr_to_nat evr.valtn e - 12)
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: ValidModel R

h1: SurjVal.v evr.valtn e.toModel.a1 ofN 1

h2: SurjVal.v evr.valtn e.toModel.a2 ofN 2

h3: SurjVal.v evr.valtn e.toModel.a3 ofN 3

h4: SurjVal.v evr.valtn e.toModel.a4 ofN 4

h6: SurjVal.v evr.valtn e.toModel.a6 ofN 6


val_discr_to_nat evr.valtn (pi_scaling evr e h1 h2 h3 h4 h6) = val_discr_to_nat evr.valtn e - 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: ValidModel R

h1: SurjVal.v evr.valtn e.toModel.a1 ofN 1

h2: SurjVal.v evr.valtn e.toModel.a2 ofN 2

h3: SurjVal.v evr.valtn e.toModel.a3 ofN 3

h4: SurjVal.v evr.valtn e.toModel.a4 ofN 4

h6: SurjVal.v evr.valtn e.toModel.a6 ofN 6


SurjVal.v evr.valtn (Model.discr (pi_scaling evr e h1 h2 h3 h4 h6).toModel) = ofN (val_discr_to_nat evr.valtn e - 12)
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: ValidModel R

h1: SurjVal.v evr.valtn e.toModel.a1 ofN 1

h2: SurjVal.v evr.valtn e.toModel.a2 ofN 2

h3: SurjVal.v evr.valtn e.toModel.a3 ofN 3

h4: SurjVal.v evr.valtn e.toModel.a4 ofN 4

h6: SurjVal.v evr.valtn e.toModel.a6 ofN 6


val_discr_to_nat evr.valtn (pi_scaling evr e h1 h2 h3 h4 h6) = val_discr_to_nat evr.valtn e - 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: ValidModel R

h1: SurjVal.v evr.valtn e.toModel.a1 ofN 1

h2: SurjVal.v evr.valtn e.toModel.a2 ofN 2

h3: SurjVal.v evr.valtn e.toModel.a3 ofN 3

h4: SurjVal.v evr.valtn e.toModel.a4 ofN 4

h6: SurjVal.v evr.valtn e.toModel.a6 ofN 6


SurjVal.v evr.valtn (Model.discr (Model.pi_scaling evr e.toModel)) = ofN (val_discr_to_nat evr.valtn e - 12)
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: ValidModel R

h1: SurjVal.v evr.valtn e.toModel.a1 ofN 1

h2: SurjVal.v evr.valtn e.toModel.a2 ofN 2

h3: SurjVal.v evr.valtn e.toModel.a3 ofN 3

h4: SurjVal.v evr.valtn e.toModel.a4 ofN 4

h6: SurjVal.v evr.valtn e.toModel.a6 ofN 6


val_discr_to_nat evr.valtn (pi_scaling evr e h1 h2 h3 h4 h6) = val_discr_to_nat evr.valtn e - 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: ValidModel R

h1: SurjVal.v evr.valtn e.toModel.a1 ofN 1

h2: SurjVal.v evr.valtn e.toModel.a2 ofN 2

h3: SurjVal.v evr.valtn e.toModel.a3 ofN 3

h4: SurjVal.v evr.valtn e.toModel.a4 ofN 4

h6: SurjVal.v evr.valtn e.toModel.a6 ofN 6


SurjVal.v evr.valtn (EnatValRing.sub_val evr (Model.discr e.toModel) 12) = ofN (val_discr_to_nat evr.valtn e - 12)
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: ValidModel R

h1: SurjVal.v evr.valtn e.toModel.a1 ofN 1

h2: SurjVal.v evr.valtn e.toModel.a2 ofN 2

h3: SurjVal.v evr.valtn e.toModel.a3 ofN 3

h4: SurjVal.v evr.valtn e.toModel.a4 ofN 4

h6: SurjVal.v evr.valtn e.toModel.a6 ofN 6


val_discr_to_nat evr.valtn (pi_scaling evr e h1 h2 h3 h4 h6) = val_discr_to_nat evr.valtn e - 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: ValidModel R

h1: SurjVal.v evr.valtn e.toModel.a1 ofN 1

h2: SurjVal.v evr.valtn e.toModel.a2 ofN 2

h3: SurjVal.v evr.valtn e.toModel.a3 ofN 3

h4: SurjVal.v evr.valtn e.toModel.a4 ofN 4

h6: SurjVal.v evr.valtn e.toModel.a6 ofN 6


ofN (?m.20488 - 12) = ofN (val_discr_to_nat evr.valtn e - 12)
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: ValidModel R

h1: SurjVal.v evr.valtn e.toModel.a1 ofN 1

h2: SurjVal.v evr.valtn e.toModel.a2 ofN 2

h3: SurjVal.v evr.valtn e.toModel.a3 ofN 3

h4: SurjVal.v evr.valtn e.toModel.a4 ofN 4

h6: SurjVal.v evr.valtn e.toModel.a6 ofN 6


h
SurjVal.v evr.valtn (Model.discr e.toModel) = ofN ?m.20488
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: ValidModel R

h1: SurjVal.v evr.valtn e.toModel.a1 ofN 1

h2: SurjVal.v evr.valtn e.toModel.a2 ofN 2

h3: SurjVal.v evr.valtn e.toModel.a3 ofN 3

h4: SurjVal.v evr.valtn e.toModel.a4 ofN 4

h6: SurjVal.v evr.valtn e.toModel.a6 ofN 6


R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: ValidModel R

h1: SurjVal.v evr.valtn e.toModel.a1 ofN 1

h2: SurjVal.v evr.valtn e.toModel.a2 ofN 2

h3: SurjVal.v evr.valtn e.toModel.a3 ofN 3

h4: SurjVal.v evr.valtn e.toModel.a4 ofN 4

h6: SurjVal.v evr.valtn e.toModel.a6 ofN 6


h
SurjVal.v evr.valtn (Model.discr e.toModel) = ofN (val_discr_to_nat evr.valtn e)
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: ValidModel R

h1: SurjVal.v evr.valtn e.toModel.a1 ofN 1

h2: SurjVal.v evr.valtn e.toModel.a2 ofN 2

h3: SurjVal.v evr.valtn e.toModel.a3 ofN 3

h4: SurjVal.v evr.valtn e.toModel.a4 ofN 4

h6: SurjVal.v evr.valtn e.toModel.a6 ofN 6


val_discr_to_nat evr.valtn (pi_scaling evr e h1 h2 h3 h4 h6) = val_discr_to_nat evr.valtn e - 12
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: ValidModel R

h1: SurjVal.v evr.valtn e.toModel.a1 ofN 1

h2: SurjVal.v evr.valtn e.toModel.a2 ofN 2

h3: SurjVal.v evr.valtn e.toModel.a3 ofN 3

h4: SurjVal.v evr.valtn e.toModel.a4 ofN 4

h6: SurjVal.v evr.valtn e.toModel.a6 ofN 6


h
SurjVal.v evr.valtn (Model.discr e.toModel) = ofN (val_discr_to_nat evr.valtn e)
R: Type u

inst: IntegralDomain R

p: R

evr: EnatValRing p

e: ValidModel R

h1: SurjVal.v evr.valtn e.toModel.a1 ofN 1

h2: SurjVal.v evr.valtn e.toModel.a2 ofN 2

h3: SurjVal.v evr.valtn e.toModel.a3 ofN 3

h4: SurjVal.v evr.valtn e.toModel.a4 ofN 4

h6: SurjVal.v evr.valtn e.toModel.a6 ofN 6


h
SurjVal.v evr.valtn (Model.discr e.toModel) = SurjVal.v evr.valtn (Model.discr e.toModel)

Goals accomplished! 🐙
lemma
v_b2_of_v_a1_a2: ∀ {R : Type u} [inst : IntegralDomain R] {p : R} (valp : SurjVal p) (e : ValidModel R), SurjVal.v valp e.toModel.a1 ofN 1SurjVal.v valp e.toModel.a2 = ofN 1SurjVal.v valp (Model.b2 e.toModel) ofN 1
v_b2_of_v_a1_a2
{
p: R
p
:
R: Type u
R
} (
valp: SurjVal p
valp
:
SurjVal: {R : Type ?u.20562} → R[inst : IntegralDomain R] → Type ?u.20562
SurjVal
p: R
p
) (e :
ValidModel: (R : Type ?u.20570) → [inst : IntegralDomain R] → Type ?u.20570
ValidModel
R: Type u
R
) (
h1: SurjVal.v valp e.toModel.a1 ofN 1
h1
:
valp: SurjVal p
valp
.
v: {R : Type ?u.20575} → {p : R} → [inst : IntegralDomain R] → SurjVal pRℕ∪∞
v
e.
a1: {R : Type ?u.20587} → [inst : IntegralDomain R] → Model RR
a1
ofN: ℕ∪∞
ofN
1: ?m.20593
1
) (
h2: SurjVal.v valp e.toModel.a2 = ofN 1
h2
:
valp: SurjVal p
valp
.
v: {R : Type ?u.20611} → {p : R} → [inst : IntegralDomain R] → SurjVal pRℕ∪∞
v
e.
a2: {R : Type ?u.20618} → [inst : IntegralDomain R] → Model RR
a2
=
ofN: ℕ∪∞
ofN
1: ?m.20622
1
) :
valp: SurjVal p
valp
.
v: {R : Type ?u.20628} → {p : R} → [inst : IntegralDomain R] → SurjVal pRℕ∪∞
v
e.
b2: {R : Type ?u.20635} → [inst : IntegralDomain R] → Model RR
b2
ofN: ℕ∪∞
ofN
1: ?m.20642
1
:=
val_add_ge_of_ge: ∀ {R : Type ?u.20657} [inst : IntegralDomain R] {n : ℕ∪∞} {p : R} (nav : SurjVal p) {a b : R}, SurjVal.v nav a nSurjVal.v nav b nSurjVal.v nav (a + b) n
val_add_ge_of_ge
valp: SurjVal p
valp
(
val_mul_ge_of_left_ge: ∀ {R : Type ?u.20682} [inst : IntegralDomain R] {n : ℕ∪∞} {p : R} (nav : SurjVal p) {a b : R}, SurjVal.v nav a nSurjVal.v nav (a * b) n
val_mul_ge_of_left_ge
valp: SurjVal p
valp
h1: SurjVal.v valp e.toModel.a1 ofN 1
h1
) (
val_mul_ge_of_right_ge: ∀ {R : Type ?u.20698} [inst : IntegralDomain R] {n : ℕ∪∞} {p : R} (nav : SurjVal p) {a b : R}, SurjVal.v nav b nSurjVal.v nav (a * b) n
val_mul_ge_of_right_ge
valp: SurjVal p
valp
(
le_of_eq: ∀ {α : Type ?u.20708} [inst : Preorder α] {a b : α}, a = ba b
le_of_eq
h2: SurjVal.v valp e.toModel.a2 = ofN 1
h2
.
symm: ∀ {α : Sort ?u.20719} {a b : α}, a = bb = a
symm
)) lemma
v_b4_of_v_a1_a3_a4: ∀ {R : Type u} [inst : IntegralDomain R] {q : } {p : R} (valp : SurjVal p) (e : ValidModel R), SurjVal.v valp e.toModel.a1 ofN 1SurjVal.v valp e.toModel.a3 ofN qSurjVal.v valp e.toModel.a4 ofN (q + 1)SurjVal.v valp (Model.b4 e.toModel) ofN (q + 1)
v_b4_of_v_a1_a3_a4
{
p: R
p
:
R: Type u
R
} (
valp: SurjVal p
valp
:
SurjVal: {R : Type ?u.20811} → R[inst : IntegralDomain R] → Type ?u.20811
SurjVal
p: R
p
) (e :
ValidModel: (R : Type ?u.20816) → [inst : IntegralDomain R] → Type ?u.20816
ValidModel
R: Type u
R
) (
h1: SurjVal.v valp e.toModel.a1 ofN 1
h1
:
valp: SurjVal p
valp
.
v: {R : Type ?u.20821} → {p : R} → [inst : IntegralDomain R] → SurjVal pRℕ∪∞
v
e.
a1: {R : Type ?u.20828} → [inst : IntegralDomain R] → Model RR
a1
ofN: ℕ∪∞
ofN
1: ?m.20832
1
) (
h3: SurjVal.v valp e.toModel.a3 ofN q
h3
:
valp: SurjVal p
valp
.
v: {R : Type ?u.20839} → {p : R} → [inst : IntegralDomain R] → SurjVal pRℕ∪∞
v
e.
a3: {R : Type ?u.20846} → [inst : IntegralDomain R] → Model RR
a3
ofN: ℕ∪∞
ofN
q: ?m.20806
q
) (
h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)
h4
:
valp: SurjVal p
valp
.
v: {R : Type ?u.20854} → {p : R} → [inst : IntegralDomain R] → SurjVal pRℕ∪∞
v
e.
a4: {R : Type ?u.20861} → [inst : IntegralDomain R] → Model RR
a4
ofN: ℕ∪∞
ofN
(
q: ?m.20806
q
+
1: ?m.20868
1
)) :
valp: SurjVal p
valp
.
v: {R : Type ?u.20925} → {p : R} → [inst : IntegralDomain R] → SurjVal pRℕ∪∞
v
e.
b4: {R : Type ?u.20932} → [inst : IntegralDomain R] → Model RR
b4
ofN: ℕ∪∞
ofN
(
q: ?m.20806
q
+
1: ?m.20942
1
) :=
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h1: SurjVal.v valp e.toModel.a1 ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)


SurjVal.v valp (Model.b4 e.toModel) ofN (q + 1)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h1: SurjVal.v valp e.toModel.a1 ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)


ha
SurjVal.v valp (e.toModel.a1 * e.toModel.a3) ofN (q + 1)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h1: SurjVal.v valp e.toModel.a1 ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)


hb
SurjVal.v valp (2 * e.toModel.a4) ofN (q + 1)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h1: SurjVal.v valp e.toModel.a1 ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)


SurjVal.v valp (Model.b4 e.toModel) ofN (q + 1)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h1: SurjVal.v valp e.toModel.a1 ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)


ha
SurjVal.v valp (e.toModel.a1 * e.toModel.a3) ofN (q + 1)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h1: SurjVal.v valp e.toModel.a1 ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)


ha
SurjVal.v valp (e.toModel.a1 * e.toModel.a3) ofN (q + 1)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h1: SurjVal.v valp e.toModel.a1 ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)


hb
SurjVal.v valp (2 * e.toModel.a4) ofN (q + 1)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h1: SurjVal.v valp e.toModel.a1 ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)


ha
SurjVal.v valp (e.toModel.a1 * e.toModel.a3) ofN (q + 1)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h1: SurjVal.v valp e.toModel.a1 ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)


ha
SurjVal.v valp (e.toModel.a1 * e.toModel.a3) ofN q + ofN 1
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h1: SurjVal.v valp e.toModel.a1 ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)


ha
SurjVal.v valp (e.toModel.a1 * e.toModel.a3) ofN (q + 1)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h1: SurjVal.v valp e.toModel.a1 ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)


ha
SurjVal.v valp (e.toModel.a1 * e.toModel.a3) ofN 1 + ofN q
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h1: SurjVal.v valp e.toModel.a1 ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)


ha
SurjVal.v valp (e.toModel.a1 * e.toModel.a3) ofN 1 + ofN q
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h1: SurjVal.v valp e.toModel.a1 ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)


ha
SurjVal.v valp (e.toModel.a1 * e.toModel.a3) ofN (q + 1)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h1: SurjVal.v valp e.toModel.a1 ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)


hb
SurjVal.v valp (2 * e.toModel.a4) ofN (q + 1)

Goals accomplished! 🐙
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h1: SurjVal.v valp e.toModel.a1 ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)


SurjVal.v valp (Model.b4 e.toModel) ofN (q + 1)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h1: SurjVal.v valp e.toModel.a1 ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)


hb
SurjVal.v valp (2 * e.toModel.a4) ofN (q + 1)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h1: SurjVal.v valp e.toModel.a1 ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)


hb
SurjVal.v valp (2 * e.toModel.a4) ofN (q + 1)

Goals accomplished! 🐙
lemma
v_b6_of_v_a3_a6: ∀ {q : } {p : R} (valp : SurjVal p) (e : ValidModel R), SurjVal.v valp e.toModel.a3 ofN qSurjVal.v valp e.toModel.a6 ofN (2 * q)SurjVal.v valp (Model.b6 e.toModel) ofN (2 * q)
v_b6_of_v_a3_a6
{
p: R
p
:
R: Type u
R
} (
valp: SurjVal p
valp
:
SurjVal: {R : Type ?u.21146} → R[inst : IntegralDomain R] → Type ?u.21146
SurjVal
p: R
p
) (e :
ValidModel: (R : Type ?u.21151) → [inst : IntegralDomain R] → Type ?u.21151
ValidModel
R: Type u
R
) (
h3: SurjVal.v valp e.toModel.a3 ofN q
h3
:
valp: SurjVal p
valp
.
v: {R : Type ?u.21156} → {p : R} → [inst : IntegralDomain R] → SurjVal pRℕ∪∞
v
e.
a3: {R : Type ?u.21163} → [inst : IntegralDomain R] → Model RR
a3
ofN: ℕ∪∞
ofN
q: ?m.21141
q
) (
h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)
h6
:
valp: SurjVal p
valp
.
v: {R : Type ?u.21174} → {p : R} → [inst : IntegralDomain R] → SurjVal pRℕ∪∞
v
e.
a6: {R : Type ?u.21181} → [inst : IntegralDomain R] → Model RR
a6
ofN: ℕ∪∞
ofN
(
2: ?m.21188
2
*
q: ?m.21141
q
)) :
valp: SurjVal p
valp
.
v: {R : Type ?u.21254} → {p : R} → [inst : IntegralDomain R] → SurjVal pRℕ∪∞
v
e.
b6: {R : Type ?u.21261} → [inst : IntegralDomain R] → Model RR
b6
ofN: ℕ∪∞
ofN
(
2: ?m.21271
2
*
q: ?m.21141
q
) :=
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h3: SurjVal.v valp e.toModel.a3 ofN q

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


SurjVal.v valp (Model.b6 e.toModel) ofN (2 * q)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h3: SurjVal.v valp e.toModel.a3 ofN q

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


ha
SurjVal.v valp (e.toModel.a3 * e.toModel.a3) ofN (2 * q)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h3: SurjVal.v valp e.toModel.a3 ofN q

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


hb
SurjVal.v valp (4 * e.toModel.a6) ofN (2 * q)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h3: SurjVal.v valp e.toModel.a3 ofN q

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


SurjVal.v valp (Model.b6 e.toModel) ofN (2 * q)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h3: SurjVal.v valp e.toModel.a3 ofN q

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


ha
SurjVal.v valp (e.toModel.a3 * e.toModel.a3) ofN (2 * q)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h3: SurjVal.v valp e.toModel.a3 ofN q

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


ha
SurjVal.v valp (e.toModel.a3 * e.toModel.a3) ofN (2 * q)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h3: SurjVal.v valp e.toModel.a3 ofN q

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


hb
SurjVal.v valp (4 * e.toModel.a6) ofN (2 * q)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h3: SurjVal.v valp e.toModel.a3 ofN q

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


ha
SurjVal.v valp (e.toModel.a3 * e.toModel.a3) ofN (2 * q)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h3: SurjVal.v valp e.toModel.a3 ofN q

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


ha
SurjVal.v valp (e.toModel.a3 * e.toModel.a3) ofN (q + q)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h3: SurjVal.v valp e.toModel.a3 ofN q

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


ha
SurjVal.v valp (e.toModel.a3 * e.toModel.a3) ofN (q + q)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h3: SurjVal.v valp e.toModel.a3 ofN q

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


ha
SurjVal.v valp (e.toModel.a3 * e.toModel.a3) ofN (2 * q)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h3: SurjVal.v valp e.toModel.a3 ofN q

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


hb
SurjVal.v valp (4 * e.toModel.a6) ofN (2 * q)

Goals accomplished! 🐙
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h3: SurjVal.v valp e.toModel.a3 ofN q

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


SurjVal.v valp (Model.b6 e.toModel) ofN (2 * q)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h3: SurjVal.v valp e.toModel.a3 ofN q

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


hb
SurjVal.v valp (4 * e.toModel.a6) ofN (2 * q)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h3: SurjVal.v valp e.toModel.a3 ofN q

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


hb
SurjVal.v valp (4 * e.toModel.a6) ofN (2 * q)

Goals accomplished! 🐙
lemma
v_b8_of_v_ai: ∀ {q : } {p : R} (valp : SurjVal p) (e : ValidModel R), SurjVal.v valp e.toModel.a1 ofN 1SurjVal.v valp e.toModel.a2 = ofN 1SurjVal.v valp e.toModel.a3 ofN qSurjVal.v valp e.toModel.a4 ofN (q + 1)SurjVal.v valp e.toModel.a6 ofN (2 * q)SurjVal.v valp (Model.b8 e.toModel) ofN (2 * q + 1)
v_b8_of_v_ai
{
p: R
p
:
R: Type u
R
} (
valp: SurjVal p
valp
:
SurjVal: {R : Type ?u.21553} → R[inst : IntegralDomain R] → Type ?u.21553
SurjVal
p: R
p
) (e :
ValidModel: (R : Type ?u.21640) → [inst : IntegralDomain R] → Type ?u.21640
ValidModel
R: Type u
R
) (
h1: SurjVal.v valp e.toModel.a1 ofN 1
h1
:
valp: SurjVal p
valp
.
v: {R : Type ?u.21645} → {p : R} → [inst : IntegralDomain R] → SurjVal pRℕ∪∞
v
e.
a1: {R : Type ?u.21652} → [inst : IntegralDomain R] → Model RR
a1
ofN: ℕ∪∞
ofN
1: ?m.21656
1
) (
h2: SurjVal.v valp e.toModel.a2 = ofN 1
h2
:
valp: SurjVal p
valp
.
v: {R : Type ?u.21663} → {p : R} → [inst : IntegralDomain R] → SurjVal pRℕ∪∞
v
e.
a2: {R : Type ?u.21670} → [inst : IntegralDomain R] → Model RR
a2
=
ofN: ℕ∪∞
ofN
1: ?m.21674
1
) (
h3: SurjVal.v valp e.toModel.a3 ofN q
h3
:
valp: SurjVal p
valp
.
v: {R : Type ?u.21680} → {p : R} → [inst : IntegralDomain R] → SurjVal pRℕ∪∞
v
e.
a3: {R : Type ?u.21687} → [inst : IntegralDomain R] → Model RR
a3
ofN: ℕ∪∞
ofN
q: ?m.21630
q
) (
h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)
h4
:
valp: SurjVal p
valp
.
v: {R : Type ?u.21695} → {p : R} → [inst : IntegralDomain R] → SurjVal pRℕ∪∞
v
e.
a4: {R : Type ?u.21702} → [inst : IntegralDomain R] → Model RR
a4
ofN: ℕ∪∞
ofN
(
q: ?m.21630
q
+
1: ?m.21709
1
)) (
h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)
h6
:
valp: SurjVal p
valp
.
v: {R : Type ?u.21766} → {p : R} → [inst : IntegralDomain R] → SurjVal pRℕ∪∞
v
e.
a6: {R : Type ?u.21773} → [inst : IntegralDomain R] → Model RR
a6
ofN: ℕ∪∞
ofN
(
2: ?m.21780
2
*
q: ?m.21630
q
)) :
valp: SurjVal p
valp
.
v: {R : Type ?u.21842} → {p : R} → [inst : IntegralDomain R] → SurjVal pRℕ∪∞
v
e.
b8: {R : Type ?u.21849} → [inst : IntegralDomain R] → Model RR
b8
ofN: ℕ∪∞
ofN
(
2: ?m.21862
2
*
q: ?m.21630
q
+
1: ?m.21872
1
) :=
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


SurjVal.v valp (Model.b8 e.toModel) ofN (2 * q + 1)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


SurjVal.v valp (e.toModel.a1 * e.toModel.a1 * e.toModel.a6 - e.toModel.a1 * e.toModel.a3 * e.toModel.a4 + 4 * e.toModel.a2 * e.toModel.a6 + e.toModel.a2 * e.toModel.a3 * e.toModel.a3 - e.toModel.a4 * e.toModel.a4) ofN (2 * q + 1)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


SurjVal.v valp (Model.b8 e.toModel) ofN (2 * q + 1)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


SurjVal.v valp (e.toModel.a1 * e.toModel.a1 * e.toModel.a6 - e.toModel.a1 * e.toModel.a3 * e.toModel.a4 + 4 * e.toModel.a2 * e.toModel.a6 + e.toModel.a2 * e.toModel.a3 * e.toModel.a3 - e.toModel.a4 * e.toModel.a4) ofN (2 * q + 1)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


SurjVal.v valp (e.toModel.a1 * e.toModel.a1 * e.toModel.a6 - e.toModel.a1 * e.toModel.a3 * e.toModel.a4 + 4 * e.toModel.a2 * e.toModel.a6 + e.toModel.a2 * e.toModel.a3 * e.toModel.a3 + -(e.toModel.a4 * e.toModel.a4)) ofN (2 * q + 1)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


SurjVal.v valp (e.toModel.a1 * e.toModel.a1 * e.toModel.a6 - e.toModel.a1 * e.toModel.a3 * e.toModel.a4 + 4 * e.toModel.a2 * e.toModel.a6 + e.toModel.a2 * e.toModel.a3 * e.toModel.a3 - e.toModel.a4 * e.toModel.a4) ofN (2 * q + 1)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


SurjVal.v valp (e.toModel.a1 * e.toModel.a1 * e.toModel.a6 + -(e.toModel.a1 * e.toModel.a3 * e.toModel.a4) + 4 * e.toModel.a2 * e.toModel.a6 + e.toModel.a2 * e.toModel.a3 * e.toModel.a3 + -(e.toModel.a4 * e.toModel.a4)) ofN (2 * q + 1)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


SurjVal.v valp (e.toModel.a1 * e.toModel.a1 * e.toModel.a6 + -(e.toModel.a1 * e.toModel.a3 * e.toModel.a4) + 4 * e.toModel.a2 * e.toModel.a6 + e.toModel.a2 * e.toModel.a3 * e.toModel.a3 + -(e.toModel.a4 * e.toModel.a4)) ofN (2 * q + 1)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


SurjVal.v valp (Model.b8 e.toModel) ofN (2 * q + 1)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


SurjVal.v valp (e.toModel.a1 * e.toModel.a1 * e.toModel.a6 + -(e.toModel.a1 * e.toModel.a3 * e.toModel.a4) + 4 * e.toModel.a2 * e.toModel.a6 + e.toModel.a2 * e.toModel.a3 * e.toModel.a3 + -(e.toModel.a4 * e.toModel.a4)) ofN (2 * q + 1)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


ha.ha.ha.ha
SurjVal.v valp (e.toModel.a1 * e.toModel.a1 * e.toModel.a6) ofN (2 * q + 1)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


ha.ha.ha.hb
SurjVal.v valp (-(e.toModel.a1 * e.toModel.a3 * e.toModel.a4)) ofN (2 * q + 1)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


ha.ha.hb
SurjVal.v valp (4 * e.toModel.a2 * e.toModel.a6) ofN (2 * q + 1)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


ha.hb
SurjVal.v valp (e.toModel.a2 * e.toModel.a3 * e.toModel.a3) ofN (2 * q + 1)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


hb
SurjVal.v valp (-(e.toModel.a4 * e.toModel.a4)) ofN (2 * q + 1)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


SurjVal.v valp (Model.b8 e.toModel) ofN (2 * q + 1)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


ha.ha.ha.ha
SurjVal.v valp (e.toModel.a1 * e.toModel.a1 * e.toModel.a6) ofN (2 * q + 1)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


ha.ha.ha.ha
SurjVal.v valp (e.toModel.a1 * e.toModel.a1 * e.toModel.a6) ofN (2 * q + 1)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


ha.ha.ha.hb
SurjVal.v valp (-(e.toModel.a1 * e.toModel.a3 * e.toModel.a4)) ofN (2 * q + 1)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


ha.ha.hb
SurjVal.v valp (4 * e.toModel.a2 * e.toModel.a6) ofN (2 * q + 1)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


ha.hb
SurjVal.v valp (e.toModel.a2 * e.toModel.a3 * e.toModel.a3) ofN (2 * q + 1)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


hb
SurjVal.v valp (-(e.toModel.a4 * e.toModel.a4)) ofN (2 * q + 1)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


ha.ha.ha.ha
SurjVal.v valp (e.toModel.a1 * e.toModel.a1 * e.toModel.a6) ofN (2 * q + 1)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


ha.ha.ha.ha
SurjVal.v valp (e.toModel.a1 * (e.toModel.a1 * e.toModel.a6)) ofN (2 * q + 1)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


ha.ha.ha.ha
SurjVal.v valp (e.toModel.a1 * e.toModel.a1 * e.toModel.a6) ofN (2 * q + 1)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


ha.ha.ha.ha
SurjVal.v valp (e.toModel.a1 * (e.toModel.a1 * e.toModel.a6)) ofN (1 + 2 * q)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


ha.ha.ha.ha
SurjVal.v valp (e.toModel.a1 * e.toModel.a1 * e.toModel.a6) ofN (2 * q + 1)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


ha.ha.ha.ha
SurjVal.v valp (e.toModel.a1 * (e.toModel.a1 * e.toModel.a6)) ofN 1 + ofN (2 * q)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


ha.ha.ha.ha
SurjVal.v valp (e.toModel.a1 * (e.toModel.a1 * e.toModel.a6)) ofN 1 + ofN (2 * q)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


ha.ha.ha.ha
SurjVal.v valp (e.toModel.a1 * e.toModel.a1 * e.toModel.a6) ofN (2 * q + 1)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


ha.ha.ha.hb
SurjVal.v valp (-(e.toModel.a1 * e.toModel.a3 * e.toModel.a4)) ofN (2 * q + 1)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


ha.ha.hb
SurjVal.v valp (4 * e.toModel.a2 * e.toModel.a6) ofN (2 * q + 1)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


ha.hb
SurjVal.v valp (e.toModel.a2 * e.toModel.a3 * e.toModel.a3) ofN (2 * q + 1)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


hb
SurjVal.v valp (-(e.toModel.a4 * e.toModel.a4)) ofN (2 * q + 1)

Goals accomplished! 🐙
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


SurjVal.v valp (Model.b8 e.toModel) ofN (2 * q + 1)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


ha.ha.ha.hb
SurjVal.v valp (-(e.toModel.a1 * e.toModel.a3 * e.toModel.a4)) ofN (2 * q + 1)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


ha.ha.ha.hb
SurjVal.v valp (-(e.toModel.a1 * e.toModel.a3 * e.toModel.a4)) ofN (2 * q + 1)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


ha.ha.hb
SurjVal.v valp (4 * e.toModel.a2 * e.toModel.a6) ofN (2 * q + 1)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


ha.hb
SurjVal.v valp (e.toModel.a2 * e.toModel.a3 * e.toModel.a3) ofN (2 * q + 1)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


hb
SurjVal.v valp (-(e.toModel.a4 * e.toModel.a4)) ofN (2 * q + 1)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


ha.ha.ha.hb
SurjVal.v valp (-(e.toModel.a1 * e.toModel.a3 * e.toModel.a4)) ofN (2 * q + 1)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


ha.ha.ha.hb
SurjVal.v valp (e.toModel.a1 * e.toModel.a3 * e.toModel.a4) ofN (2 * q + 1)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


ha.ha.ha.hb
SurjVal.v valp (-(e.toModel.a1 * e.toModel.a3 * e.toModel.a4)) ofN (2 * q + 1)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


ha.ha.ha.hb
SurjVal.v valp (e.toModel.a1 * (e.toModel.a3 * e.toModel.a4)) ofN (2 * q + 1)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


ha.ha.ha.hb
SurjVal.v valp (-(e.toModel.a1 * e.toModel.a3 * e.toModel.a4)) ofN (2 * q + 1)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


ha.ha.ha.hb
SurjVal.v valp (e.toModel.a1 * (e.toModel.a3 * e.toModel.a4)) ofN (q + q + 1)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


ha.ha.ha.hb
SurjVal.v valp (-(e.toModel.a1 * e.toModel.a3 * e.toModel.a4)) ofN (2 * q + 1)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


ha.ha.ha.hb
SurjVal.v valp (e.toModel.a1 * (e.toModel.a3 * e.toModel.a4)) ofN (q + (q + 1))
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


ha.ha.ha.hb
SurjVal.v valp (-(e.toModel.a1 * e.toModel.a3 * e.toModel.a4)) ofN (2 * q + 1)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


ha.ha.ha.hb
SurjVal.v valp (e.toModel.a1 * (e.toModel.a3 * e.toModel.a4)) ofN q + ofN (q + 1)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


ha.ha.ha.hb
SurjVal.v valp (e.toModel.a1 * (e.toModel.a3 * e.toModel.a4)) ofN q + ofN (q + 1)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


ha.ha.ha.hb
SurjVal.v valp (-(e.toModel.a1 * e.toModel.a3 * e.toModel.a4)) ofN (2 * q + 1)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


ha.ha.hb
SurjVal.v valp (4 * e.toModel.a2 * e.toModel.a6) ofN (2 * q + 1)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


ha.hb
SurjVal.v valp (e.toModel.a2 * e.toModel.a3 * e.toModel.a3) ofN (2 * q + 1)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


hb
SurjVal.v valp (-(e.toModel.a4 * e.toModel.a4)) ofN (2 * q + 1)

Goals accomplished! 🐙
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


SurjVal.v valp (Model.b8 e.toModel) ofN (2 * q + 1)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


ha.ha.hb
SurjVal.v valp (4 * e.toModel.a2 * e.toModel.a6) ofN (2 * q + 1)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


ha.ha.hb
SurjVal.v valp (4 * e.toModel.a2 * e.toModel.a6) ofN (2 * q + 1)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


ha.hb
SurjVal.v valp (e.toModel.a2 * e.toModel.a3 * e.toModel.a3) ofN (2 * q + 1)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


hb
SurjVal.v valp (-(e.toModel.a4 * e.toModel.a4)) ofN (2 * q + 1)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


ha.ha.hb
SurjVal.v valp (4 * e.toModel.a2 * e.toModel.a6) ofN (2 * q + 1)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


ha.ha.hb
SurjVal.v valp (4 * (e.toModel.a2 * e.toModel.a6)) ofN (2 * q + 1)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


ha.ha.hb
SurjVal.v valp (4 * e.toModel.a2 * e.toModel.a6) ofN (2 * q + 1)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


ha.ha.hb
SurjVal.v valp (4 * (e.toModel.a2 * e.toModel.a6)) ofN (1 + 2 * q)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


ha.ha.hb
SurjVal.v valp (4 * e.toModel.a2 * e.toModel.a6) ofN (2 * q + 1)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


ha.ha.hb
SurjVal.v valp (4 * (e.toModel.a2 * e.toModel.a6)) ofN 1 + ofN (2 * q)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


ha.ha.hb
SurjVal.v valp (4 * (e.toModel.a2 * e.toModel.a6)) ofN 1 + ofN (2 * q)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


ha.ha.hb
SurjVal.v valp (4 * e.toModel.a2 * e.toModel.a6) ofN (2 * q + 1)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


ha.hb
SurjVal.v valp (e.toModel.a2 * e.toModel.a3 * e.toModel.a3) ofN (2 * q + 1)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


hb
SurjVal.v valp (-(e.toModel.a4 * e.toModel.a4)) ofN (2 * q + 1)

Goals accomplished! 🐙
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


SurjVal.v valp (Model.b8 e.toModel) ofN (2 * q + 1)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


ha.hb
SurjVal.v valp (e.toModel.a2 * e.toModel.a3 * e.toModel.a3) ofN (2 * q + 1)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


ha.hb
SurjVal.v valp (e.toModel.a2 * e.toModel.a3 * e.toModel.a3) ofN (2 * q + 1)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


hb
SurjVal.v valp (-(e.toModel.a4 * e.toModel.a4)) ofN (2 * q + 1)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


ha.hb
SurjVal.v valp (e.toModel.a2 * e.toModel.a3 * e.toModel.a3) ofN (2 * q + 1)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


ha.hb
SurjVal.v valp (e.toModel.a2 * (e.toModel.a3 * e.toModel.a3)) ofN (2 * q + 1)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


ha.hb
SurjVal.v valp (e.toModel.a2 * e.toModel.a3 * e.toModel.a3) ofN (2 * q + 1)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


ha.hb
SurjVal.v valp (e.toModel.a2 * (e.toModel.a3 * e.toModel.a3)) ofN (q + q + 1)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


ha.hb
SurjVal.v valp (e.toModel.a2 * e.toModel.a3 * e.toModel.a3) ofN (2 * q + 1)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


ha.hb
SurjVal.v valp (e.toModel.a2 * (e.toModel.a3 * e.toModel.a3)) ofN (1 + (q + q))
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


ha.hb
SurjVal.v valp (e.toModel.a2 * e.toModel.a3 * e.toModel.a3) ofN (2 * q + 1)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


ha.hb
SurjVal.v valp (e.toModel.a2 * (e.toModel.a3 * e.toModel.a3)) ofN 1 + ofN (q + q)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


ha.hb
SurjVal.v valp (e.toModel.a2 * e.toModel.a3 * e.toModel.a3) ofN (2 * q + 1)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


ha.hb
SurjVal.v valp (e.toModel.a2 * (e.toModel.a3 * e.toModel.a3)) ofN 1 + (ofN q + ofN q)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


ha.hb
SurjVal.v valp (e.toModel.a2 * (e.toModel.a3 * e.toModel.a3)) ofN 1 + (ofN q + ofN q)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


ha.hb
SurjVal.v valp (e.toModel.a2 * e.toModel.a3 * e.toModel.a3) ofN (2 * q + 1)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


hb
SurjVal.v valp (-(e.toModel.a4 * e.toModel.a4)) ofN (2 * q + 1)

Goals accomplished! 🐙
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


SurjVal.v valp (Model.b8 e.toModel) ofN (2 * q + 1)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


hb
SurjVal.v valp (-(e.toModel.a4 * e.toModel.a4)) ofN (2 * q + 1)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


hb
SurjVal.v valp (-(e.toModel.a4 * e.toModel.a4)) ofN (2 * q + 1)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


hb
SurjVal.v valp (-(e.toModel.a4 * e.toModel.a4)) ofN (2 * q + 1)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


hb
SurjVal.v valp (e.toModel.a4 * e.toModel.a4) ofN (2 * q + 1)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


hb
SurjVal.v valp (-(e.toModel.a4 * e.toModel.a4)) ofN (2 * q + 1)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


hb
SurjVal.v valp (e.toModel.a4 * e.toModel.a4) ofN (q + q + 1)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


hb
SurjVal.v valp (-(e.toModel.a4 * e.toModel.a4)) ofN (2 * q + 1)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


hb
SurjVal.v valp (e.toModel.a4 * e.toModel.a4) ofN (q + (q + 1))
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


hb
SurjVal.v valp (-(e.toModel.a4 * e.toModel.a4)) ofN (2 * q + 1)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


hb
SurjVal.v valp (e.toModel.a4 * e.toModel.a4) ofN q + ofN (q + 1)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


hb
SurjVal.v valp (e.toModel.a4 * e.toModel.a4) ofN q + ofN (q + 1)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


hb
SurjVal.v valp (-(e.toModel.a4 * e.toModel.a4)) ofN (2 * q + 1)

Goals accomplished! 🐙
lemma
v_discr_of_v_ai: ∀ {q : } {p : R} (valp : SurjVal p) (e : ValidModel R), q > 1SurjVal.v valp e.toModel.a1 ofN 1SurjVal.v valp e.toModel.a2 = ofN 1SurjVal.v valp e.toModel.a3 ofN qSurjVal.v valp e.toModel.a4 ofN (q + 1)SurjVal.v valp e.toModel.a6 ofN (2 * q)SurjVal.v valp (Model.discr e.toModel) ofN (2 * q + 3)
v_discr_of_v_ai
{
p: R
p
:
R: Type u
R
} (
valp: SurjVal p
valp
:
SurjVal: {R : Type ?u.23189} → R[inst : IntegralDomain R] → Type ?u.23189
SurjVal
p: R
p
) (e :
ValidModel: (R : Type ?u.23213) → [inst : IntegralDomain R] → Type ?u.23213
ValidModel
R: Type u
R
) (
hq: q > 1
hq
:
q: ?m.23203
q
>
1: ?m.23219
1
) (
h1: SurjVal.v valp e.toModel.a1 ofN 1
h1
:
valp: SurjVal p
valp
.
v: {R : Type ?u.23256} → {p : R} → [inst : IntegralDomain R] → SurjVal pRℕ∪∞
v
e.
a1: {R : Type ?u.23268} → [inst : IntegralDomain R] → Model RR
a1
ofN: ℕ∪∞
ofN
1: ?m.23274
1
) (
h2: SurjVal.v valp e.toModel.a2 = ofN 1
h2
:
valp: SurjVal p
valp
.
v: {R : Type ?u.23292} → {p : R} → [inst : IntegralDomain R] → SurjVal pRℕ∪∞
v
e.
a2: {R : Type ?u.23299} → [inst : IntegralDomain R] → Model RR
a2
=
ofN: ℕ∪∞
ofN
1: ?m.23303
1
) (
h3: SurjVal.v valp e.toModel.a3 ofN q
h3
:
valp: SurjVal p
valp
.
v: {R : Type ?u.23309} → {p : R} → [inst : IntegralDomain R] → SurjVal pRℕ∪∞
v
e.
a3: {R : Type ?u.23316} → [inst : IntegralDomain R] → Model RR
a3
ofN: ℕ∪∞
ofN
q: ?m.23203
q
) (
h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)
h4
:
valp: SurjVal p
valp
.
v: {R : Type ?u.23324} → {p : R} → [inst : IntegralDomain R] → SurjVal pRℕ∪∞
v
e.
a4: {R : Type ?u.23331} → [inst : IntegralDomain R] → Model RR
a4
ofN: ℕ∪∞
ofN
(
q: ?m.23203
q
+
1: ?m.23338
1
)) (
h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)
h6
:
valp: SurjVal p
valp
.
v: {R : Type ?u.23395} → {p : R} → [inst : IntegralDomain R] → SurjVal pRℕ∪∞
v
e.
a6: {R : Type ?u.23402} → [inst : IntegralDomain R] → Model RR
a6
ofN: ℕ∪∞
ofN
(
2: ?m.23409
2
*
q: ?m.23203
q
)) :
valp: SurjVal p
valp
.
v: {R : Type ?u.23471} → {p : R} → [inst : IntegralDomain R] → SurjVal pRℕ∪∞
v
e.
discr: {R : Type ?u.23478} → [inst : IntegralDomain R] → Model RR
discr
ofN: ℕ∪∞
ofN
(
2: ?m.23491
2
*
q: ?m.23203
q
+
3: ?m.23501
3
) :=
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

hq: q > 1

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


SurjVal.v valp (Model.discr e.toModel) ofN (2 * q + 3)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

hq: q > 1

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)

h2': SurjVal.v valp (Model.b2 e.toModel) ofN 1


SurjVal.v valp (Model.discr e.toModel) ofN (2 * q + 3)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

hq: q > 1

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


SurjVal.v valp (Model.discr e.toModel) ofN (2 * q + 3)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

hq: q > 1

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)

h2': SurjVal.v valp (Model.b2 e.toModel) ofN 1

h4': SurjVal.v valp (Model.b4 e.toModel) ofN (q + 1)


SurjVal.v valp (Model.discr e.toModel) ofN (2 * q + 3)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

hq: q > 1

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


SurjVal.v valp (Model.discr e.toModel) ofN (2 * q + 3)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

hq: q > 1

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)

h2': SurjVal.v valp (Model.b2 e.toModel) ofN 1

h4': SurjVal.v valp (Model.b4 e.toModel) ofN (q + 1)

h6': SurjVal.v valp (Model.b6 e.toModel) ofN (2 * q)


SurjVal.v valp (Model.discr e.toModel) ofN (2 * q + 3)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

hq: q > 1

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


SurjVal.v valp (Model.discr e.toModel) ofN (2 * q + 3)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

hq: q > 1

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)

h2': SurjVal.v valp (Model.b2 e.toModel) ofN 1

h4': SurjVal.v valp (Model.b4 e.toModel) ofN (q + 1)

h6': SurjVal.v valp (Model.b6 e.toModel) ofN (2 * q)

h8': SurjVal.v valp (Model.b8 e.toModel) ofN (2 * q + 1)


SurjVal.v valp (Model.discr e.toModel) ofN (2 * q + 3)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

hq: q > 1

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


SurjVal.v valp (Model.discr e.toModel) ofN (2 * q + 3)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

hq: q > 1

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)

h2': SurjVal.v valp (Model.b2 e.toModel) ofN 1

h4': SurjVal.v valp (Model.b4 e.toModel) ofN (q + 1)

h6': SurjVal.v valp (Model.b6 e.toModel) ofN (2 * q)

h8': SurjVal.v valp (Model.b8 e.toModel) ofN (2 * q + 1)


SurjVal.v valp (-Model.b2 e.toModel * Model.b2 e.toModel * Model.b8 e.toModel - 8 * Model.b4 e.toModel ^ 3 - 27 * Model.b6 e.toModel * Model.b6 e.toModel + 9 * Model.b2 e.toModel * Model.b4 e.toModel * Model.b6 e.toModel) ofN (2 * q + 3)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

hq: q > 1

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


SurjVal.v valp (Model.discr e.toModel) ofN (2 * q + 3)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

hq: q > 1

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)

h2': SurjVal.v valp (Model.b2 e.toModel) ofN 1

h4': SurjVal.v valp (Model.b4 e.toModel) ofN (q + 1)

h6': SurjVal.v valp (Model.b6 e.toModel) ofN (2 * q)

h8': SurjVal.v valp (Model.b8 e.toModel) ofN (2 * q + 1)


SurjVal.v valp (-Model.b2 e.toModel * Model.b2 e.toModel * Model.b8 e.toModel - 8 * Model.b4 e.toModel ^ 3 - 27 * Model.b6 e.toModel * Model.b6 e.toModel + 9 * Model.b2 e.toModel * Model.b4 e.toModel * Model.b6 e.toModel) ofN (2 * q + 3)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

hq: q > 1

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)

h2': SurjVal.v valp (Model.b2 e.toModel) ofN 1

h4': SurjVal.v valp (Model.b4 e.toModel) ofN (q + 1)

h6': SurjVal.v valp (Model.b6 e.toModel) ofN (2 * q)

h8': SurjVal.v valp (Model.b8 e.toModel) ofN (2 * q + 1)


SurjVal.v valp (-Model.b2 e.toModel * Model.b2 e.toModel * Model.b8 e.toModel - 8 * Model.b4 e.toModel ^ 3 + -(27 * Model.b6 e.toModel * Model.b6 e.toModel) + 9 * Model.b2 e.toModel * Model.b4 e.toModel * Model.b6 e.toModel) ofN (2 * q + 3)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

hq: q > 1

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)

h2': SurjVal.v valp (Model.b2 e.toModel) ofN 1

h4': SurjVal.v valp (Model.b4 e.toModel) ofN (q + 1)

h6': SurjVal.v valp (Model.b6 e.toModel) ofN (2 * q)

h8': SurjVal.v valp (Model.b8 e.toModel) ofN (2 * q + 1)


SurjVal.v valp (-Model.b2 e.toModel * Model.b2 e.toModel * Model.b8 e.toModel - 8 * Model.b4 e.toModel ^ 3 - 27 * Model.b6 e.toModel * Model.b6 e.toModel + 9 * Model.b2 e.toModel * Model.b4 e.toModel * Model.b6 e.toModel) ofN (2 * q + 3)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

hq: q > 1

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)

h2': SurjVal.v valp (Model.b2 e.toModel) ofN 1

h4': SurjVal.v valp (Model.b4 e.toModel) ofN (q + 1)

h6': SurjVal.v valp (Model.b6 e.toModel) ofN (2 * q)

h8': SurjVal.v valp (Model.b8 e.toModel) ofN (2 * q + 1)


SurjVal.v valp (-Model.b2 e.toModel * Model.b2 e.toModel * Model.b8 e.toModel + -(8 * Model.b4 e.toModel ^ 3) + -(27 * Model.b6 e.toModel * Model.b6 e.toModel) + 9 * Model.b2 e.toModel * Model.b4 e.toModel * Model.b6 e.toModel) ofN (2 * q + 3)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

hq: q > 1

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)

h2': SurjVal.v valp (Model.b2 e.toModel) ofN 1

h4': SurjVal.v valp (Model.b4 e.toModel) ofN (q + 1)

h6': SurjVal.v valp (Model.b6 e.toModel) ofN (2 * q)

h8': SurjVal.v valp (Model.b8 e.toModel) ofN (2 * q + 1)


SurjVal.v valp (-Model.b2 e.toModel * Model.b2 e.toModel * Model.b8 e.toModel + -(8 * Model.b4 e.toModel ^ 3) + -(27 * Model.b6 e.toModel * Model.b6 e.toModel) + 9 * Model.b2 e.toModel * Model.b4 e.toModel * Model.b6 e.toModel) ofN (2 * q + 3)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

hq: q > 1

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


SurjVal.v valp (Model.discr e.toModel) ofN (2 * q + 3)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

hq: q > 1

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)

h2': SurjVal.v valp (Model.b2 e.toModel) ofN 1

h4': SurjVal.v valp (Model.b4 e.toModel) ofN (q + 1)

h6': SurjVal.v valp (Model.b6 e.toModel) ofN (2 * q)

h8': SurjVal.v valp (Model.b8 e.toModel) ofN (2 * q + 1)


ha
SurjVal.v valp (-Model.b2 e.toModel * Model.b2 e.toModel * Model.b8 e.toModel + -(8 * Model.b4 e.toModel ^ 3) + -(27 * Model.b6 e.toModel * Model.b6 e.toModel)) ofN (2 * q + 3)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

hq: q > 1

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)

h2': SurjVal.v valp (Model.b2 e.toModel) ofN 1

h4': SurjVal.v valp (Model.b4 e.toModel) ofN (q + 1)

h6': SurjVal.v valp (Model.b6 e.toModel) ofN (2 * q)

h8': SurjVal.v valp (Model.b8 e.toModel) ofN (2 * q + 1)


hb
SurjVal.v valp (9 * Model.b2 e.toModel * Model.b4 e.toModel * Model.b6 e.toModel) ofN (2 * q + 3)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

hq: q > 1

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


SurjVal.v valp (Model.discr e.toModel) ofN (2 * q + 3)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

hq: q > 1

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)

h2': SurjVal.v valp (Model.b2 e.toModel) ofN 1

h4': SurjVal.v valp (Model.b4 e.toModel) ofN (q + 1)

h6': SurjVal.v valp (Model.b6 e.toModel) ofN (2 * q)

h8': SurjVal.v valp (Model.b8 e.toModel) ofN (2 * q + 1)


ha
SurjVal.v valp (-Model.b2 e.toModel * Model.b2 e.toModel * Model.b8 e.toModel + -(8 * Model.b4 e.toModel ^ 3) + -(27 * Model.b6 e.toModel * Model.b6 e.toModel)) ofN (2 * q + 3)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

hq: q > 1

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)

h2': SurjVal.v valp (Model.b2 e.toModel) ofN 1

h4': SurjVal.v valp (Model.b4 e.toModel) ofN (q + 1)

h6': SurjVal.v valp (Model.b6 e.toModel) ofN (2 * q)

h8': SurjVal.v valp (Model.b8 e.toModel) ofN (2 * q + 1)


ha
SurjVal.v valp (-Model.b2 e.toModel * Model.b2 e.toModel * Model.b8 e.toModel + -(8 * Model.b4 e.toModel ^ 3) + -(27 * Model.b6 e.toModel * Model.b6 e.toModel)) ofN (2 * q + 3)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

hq: q > 1

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)

h2': SurjVal.v valp (Model.b2 e.toModel) ofN 1

h4': SurjVal.v valp (Model.b4 e.toModel) ofN (q + 1)

h6': SurjVal.v valp (Model.b6 e.toModel) ofN (2 * q)

h8': SurjVal.v valp (Model.b8 e.toModel) ofN (2 * q + 1)


hb
SurjVal.v valp (9 * Model.b2 e.toModel * Model.b4 e.toModel * Model.b6 e.toModel) ofN (2 * q + 3)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

hq: q > 1

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)

h2': SurjVal.v valp (Model.b2 e.toModel) ofN 1

h4': SurjVal.v valp (Model.b4 e.toModel) ofN (q + 1)

h6': SurjVal.v valp (Model.b6 e.toModel) ofN (2 * q)

h8': SurjVal.v valp (Model.b8 e.toModel) ofN (2 * q + 1)


ha.ha
SurjVal.v valp (-Model.b2 e.toModel * Model.b2 e.toModel * Model.b8 e.toModel + -(8 * Model.b4 e.toModel ^ 3)) ofN (2 * q + 3)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

hq: q > 1

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)

h2': SurjVal.v valp (Model.b2 e.toModel) ofN 1

h4': SurjVal.v valp (Model.b4 e.toModel) ofN (q + 1)

h6': SurjVal.v valp (Model.b6 e.toModel) ofN (2 * q)

h8': SurjVal.v valp (Model.b8 e.toModel) ofN (2 * q + 1)


ha.hb
SurjVal.v valp (-(27 * Model.b6 e.toModel * Model.b6 e.toModel)) ofN (2 * q + 3)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

hq: q > 1

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)

h2': SurjVal.v valp (Model.b2 e.toModel) ofN 1

h4': SurjVal.v valp (Model.b4 e.toModel) ofN (q + 1)

h6': SurjVal.v valp (Model.b6 e.toModel) ofN (2 * q)

h8': SurjVal.v valp (Model.b8 e.toModel) ofN (2 * q + 1)


ha
SurjVal.v valp (-Model.b2 e.toModel * Model.b2 e.toModel * Model.b8 e.toModel + -(8 * Model.b4 e.toModel ^ 3) + -(27 * Model.b6 e.toModel * Model.b6 e.toModel)) ofN (2 * q + 3)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

hq: q > 1

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)

h2': SurjVal.v valp (Model.b2 e.toModel) ofN 1

h4': SurjVal.v valp (Model.b4 e.toModel) ofN (q + 1)

h6': SurjVal.v valp (Model.b6 e.toModel) ofN (2 * q)

h8': SurjVal.v valp (Model.b8 e.toModel) ofN (2 * q + 1)


hb
SurjVal.v valp (9 * Model.b2 e.toModel * Model.b4 e.toModel * Model.b6 e.toModel) ofN (2 * q + 3)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

hq: q > 1

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)

h2': SurjVal.v valp (Model.b2 e.toModel) ofN 1

h4': SurjVal.v valp (Model.b4 e.toModel) ofN (q + 1)

h6': SurjVal.v valp (Model.b6 e.toModel) ofN (2 * q)

h8': SurjVal.v valp (Model.b8 e.toModel) ofN (2 * q + 1)


ha.ha
SurjVal.v valp (-Model.b2 e.toModel * Model.b2 e.toModel * Model.b8 e.toModel + -(8 * Model.b4 e.toModel ^ 3)) ofN (2 * q + 3)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

hq: q > 1

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)

h2': SurjVal.v valp (Model.b2 e.toModel) ofN 1

h4': SurjVal.v valp (Model.b4 e.toModel) ofN (q + 1)

h6': SurjVal.v valp (Model.b6 e.toModel) ofN (2 * q)

h8': SurjVal.v valp (Model.b8 e.toModel) ofN (2 * q + 1)


ha.ha
SurjVal.v valp (-Model.b2 e.toModel * Model.b2 e.toModel * Model.b8 e.toModel + -(8 * Model.b4 e.toModel ^ 3)) ofN (2 * q + 3)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

hq: q > 1

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)

h2': SurjVal.v valp (Model.b2 e.toModel) ofN 1

h4': SurjVal.v valp (Model.b4 e.toModel) ofN (q + 1)

h6': SurjVal.v valp (Model.b6 e.toModel) ofN (2 * q)

h8': SurjVal.v valp (Model.b8 e.toModel) ofN (2 * q + 1)


ha.hb
SurjVal.v valp (-(27 * Model.b6 e.toModel * Model.b6 e.toModel)) ofN (2 * q + 3)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

hq: q > 1

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)

h2': SurjVal.v valp (Model.b2 e.toModel) ofN 1

h4': SurjVal.v valp (Model.b4 e.toModel) ofN (q + 1)

h6': SurjVal.v valp (Model.b6 e.toModel) ofN (2 * q)

h8': SurjVal.v valp (Model.b8 e.toModel) ofN (2 * q + 1)


ha.ha.ha
SurjVal.v valp (-Model.b2 e.toModel * Model.b2 e.toModel * Model.b8 e.toModel) ofN (2 * q + 3)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

hq: q > 1

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)

h2': SurjVal.v valp (Model.b2 e.toModel) ofN 1

h4': SurjVal.v valp (Model.b4 e.toModel) ofN (q + 1)

h6': SurjVal.v valp (Model.b6 e.toModel) ofN (2 * q)

h8': SurjVal.v valp (Model.b8 e.toModel) ofN (2 * q + 1)


ha.ha.hb
SurjVal.v valp (-(8 * Model.b4 e.toModel ^ 3)) ofN (2 * q + 3)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

hq: q > 1

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)

h2': SurjVal.v valp (Model.b2 e.toModel) ofN 1

h4': SurjVal.v valp (Model.b4 e.toModel) ofN (q + 1)

h6': SurjVal.v valp (Model.b6 e.toModel) ofN (2 * q)

h8': SurjVal.v valp (Model.b8 e.toModel) ofN (2 * q + 1)


ha.ha
SurjVal.v valp (-Model.b2 e.toModel * Model.b2 e.toModel * Model.b8 e.toModel + -(8 * Model.b4 e.toModel ^ 3)) ofN (2 * q + 3)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

hq: q > 1

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)

h2': SurjVal.v valp (Model.b2 e.toModel) ofN 1

h4': SurjVal.v valp (Model.b4 e.toModel) ofN (q + 1)

h6': SurjVal.v valp (Model.b6 e.toModel) ofN (2 * q)

h8': SurjVal.v valp (Model.b8 e.toModel) ofN (2 * q + 1)


ha.hb
SurjVal.v valp (-(27 * Model.b6 e.toModel * Model.b6 e.toModel)) ofN (2 * q + 3)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

hq: q > 1

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)

h2': SurjVal.v valp (Model.b2 e.toModel) ofN 1

h4': SurjVal.v valp (Model.b4 e.toModel) ofN (q + 1)

h6': SurjVal.v valp (Model.b6 e.toModel) ofN (2 * q)

h8': SurjVal.v valp (Model.b8 e.toModel) ofN (2 * q + 1)


ha.ha.ha
SurjVal.v valp (-Model.b2 e.toModel * Model.b2 e.toModel * Model.b8 e.toModel) ofN (2 * q + 3)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

hq: q > 1

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)

h2': SurjVal.v valp (Model.b2 e.toModel) ofN 1

h4': SurjVal.v valp (Model.b4 e.toModel) ofN (q + 1)

h6': SurjVal.v valp (Model.b6 e.toModel) ofN (2 * q)

h8': SurjVal.v valp (Model.b8 e.toModel) ofN (2 * q + 1)


ha.ha.ha
SurjVal.v valp (-Model.b2 e.toModel * Model.b2 e.toModel * Model.b8 e.toModel) ofN (2 * q + 3)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

hq: q > 1

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)

h2': SurjVal.v valp (Model.b2 e.toModel) ofN 1

h4': SurjVal.v valp (Model.b4 e.toModel) ofN (q + 1)

h6': SurjVal.v valp (Model.b6 e.toModel) ofN (2 * q)

h8': SurjVal.v valp (Model.b8 e.toModel) ofN (2 * q + 1)


ha.ha.hb
SurjVal.v valp (-(8 * Model.b4 e.toModel ^ 3)) ofN (2 * q + 3)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

hq: q > 1

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)

h2': SurjVal.v valp (Model.b2 e.toModel) ofN 1

h4': SurjVal.v valp (Model.b4 e.toModel) ofN (q + 1)

h6': SurjVal.v valp (Model.b6 e.toModel) ofN (2 * q)

h8': SurjVal.v valp (Model.b8 e.toModel) ofN (2 * q + 1)


ha.ha.ha
SurjVal.v valp (-Model.b2 e.toModel * Model.b2 e.toModel * Model.b8 e.toModel) ofN (2 * q + 3)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

hq: q > 1

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)

h2': SurjVal.v valp (Model.b2 e.toModel) ofN 1

h4': SurjVal.v valp (Model.b4 e.toModel) ofN (q + 1)

h6': SurjVal.v valp (Model.b6 e.toModel) ofN (2 * q)

h8': SurjVal.v valp (Model.b8 e.toModel) ofN (2 * q + 1)


ha.ha.ha
SurjVal.v valp (-(Model.b2 e.toModel * Model.b2 e.toModel) * Model.b8 e.toModel) ofN (2 * q + 3)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

hq: q > 1

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)

h2': SurjVal.v valp (Model.b2 e.toModel) ofN 1

h4': SurjVal.v valp (Model.b4 e.toModel) ofN (q + 1)

h6': SurjVal.v valp (Model.b6 e.toModel) ofN (2 * q)

h8': SurjVal.v valp (Model.b8 e.toModel) ofN (2 * q + 1)


ha.ha.ha
SurjVal.v valp (-Model.b2 e.toModel * Model.b2 e.toModel * Model.b8 e.toModel) ofN (2 * q + 3)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

hq: q > 1

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)

h2': SurjVal.v valp (Model.b2 e.toModel) ofN 1

h4': SurjVal.v valp (Model.b4 e.toModel) ofN (q + 1)

h6': SurjVal.v valp (Model.b6 e.toModel) ofN (2 * q)

h8': SurjVal.v valp (Model.b8 e.toModel) ofN (2 * q + 1)


ha.ha.ha
SurjVal.v valp (-(Model.b2 e.toModel * Model.b2 e.toModel * Model.b8 e.toModel)) ofN (2 * q + 3)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

hq: q > 1

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)

h2': SurjVal.v valp (Model.b2 e.toModel) ofN 1

h4': SurjVal.v valp (Model.b4 e.toModel) ofN (q + 1)

h6': SurjVal.v valp (Model.b6 e.toModel) ofN (2 * q)

h8': SurjVal.v valp (Model.b8 e.toModel) ofN (2 * q + 1)


ha.ha.ha
SurjVal.v valp (-Model.b2 e.toModel * Model.b2 e.toModel * Model.b8 e.toModel) ofN (2 * q + 3)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

hq: q > 1

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)

h2': SurjVal.v valp (Model.b2 e.toModel) ofN 1

h4': SurjVal.v valp (Model.b4 e.toModel) ofN (q + 1)

h6': SurjVal.v valp (Model.b6 e.toModel) ofN (2 * q)

h8': SurjVal.v valp (Model.b8 e.toModel) ofN (2 * q + 1)


ha.ha.ha
SurjVal.v valp (Model.b2 e.toModel * Model.b2 e.toModel * Model.b8 e.toModel) ofN (2 * q + 3)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

hq: q > 1

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)

h2': SurjVal.v valp (Model.b2 e.toModel) ofN 1

h4': SurjVal.v valp (Model.b4 e.toModel) ofN (q + 1)

h6': SurjVal.v valp (Model.b6 e.toModel) ofN (2 * q)

h8': SurjVal.v valp (Model.b8 e.toModel) ofN (2 * q + 1)


ha.ha.ha
SurjVal.v valp (-Model.b2 e.toModel * Model.b2 e.toModel * Model.b8 e.toModel) ofN (2 * q + 3)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

hq: q > 1

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)

h2': SurjVal.v valp (Model.b2 e.toModel) ofN 1

h4': SurjVal.v valp (Model.b4 e.toModel) ofN (q + 1)

h6': SurjVal.v valp (Model.b6 e.toModel) ofN (2 * q)

h8': SurjVal.v valp (Model.b8 e.toModel) ofN (2 * q + 1)


ha.ha.ha
SurjVal.v valp (Model.b2 e.toModel * Model.b2 e.toModel * Model.b8 e.toModel) ofN (2 * q + 3)

Goals accomplished! 🐙
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

hq: q > 1

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)

h2': SurjVal.v valp (Model.b2 e.toModel) ofN 1

h4': SurjVal.v valp (Model.b4 e.toModel) ofN (q + 1)

h6': SurjVal.v valp (Model.b6 e.toModel) ofN (2 * q)

h8': SurjVal.v valp (Model.b8 e.toModel) ofN (2 * q + 1)


ha.ha.ha
SurjVal.v valp (Model.b2 e.toModel * Model.b2 e.toModel * Model.b8 e.toModel) ofN (2 * q + (1 + 1 + 1))
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

hq: q > 1

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)

h2': SurjVal.v valp (Model.b2 e.toModel) ofN 1

h4': SurjVal.v valp (Model.b4 e.toModel) ofN (q + 1)

h6': SurjVal.v valp (Model.b6 e.toModel) ofN (2 * q)

h8': SurjVal.v valp (Model.b8 e.toModel) ofN (2 * q + 1)


ha.ha.ha
SurjVal.v valp (-Model.b2 e.toModel * Model.b2 e.toModel * Model.b8 e.toModel) ofN (2 * q + 3)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

hq: q > 1

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)

h2': SurjVal.v valp (Model.b2 e.toModel) ofN 1

h4': SurjVal.v valp (Model.b4 e.toModel) ofN (q + 1)

h6': SurjVal.v valp (Model.b6 e.toModel) ofN (2 * q)

h8': SurjVal.v valp (Model.b8 e.toModel) ofN (2 * q + 1)


ha.ha.ha
SurjVal.v valp (Model.b2 e.toModel * Model.b2 e.toModel * Model.b8 e.toModel) ofN (2 * q + (1 + 1) + 1)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

hq: q > 1

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)

h2': SurjVal.v valp (Model.b2 e.toModel) ofN 1

h4': SurjVal.v valp (Model.b4 e.toModel) ofN (q + 1)

h6': SurjVal.v valp (Model.b6 e.toModel) ofN (2 * q)

h8': SurjVal.v valp (Model.b8 e.toModel) ofN (2 * q + 1)


ha.ha.ha
SurjVal.v valp (-Model.b2 e.toModel * Model.b2 e.toModel * Model.b8 e.toModel) ofN (2 * q + 3)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

hq: q > 1

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)

h2': SurjVal.v valp (Model.b2 e.toModel) ofN 1

h4': SurjVal.v valp (Model.b4 e.toModel) ofN (q + 1)

h6': SurjVal.v valp (Model.b6 e.toModel) ofN (2 * q)

h8': SurjVal.v valp (Model.b8 e.toModel) ofN (2 * q + 1)


ha.ha.ha
SurjVal.v valp (Model.b2 e.toModel * Model.b2 e.toModel * Model.b8 e.toModel) ofN (2 * q + 1 + 1 + 1)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

hq: q > 1

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)

h2': SurjVal.v valp (Model.b2 e.toModel) ofN 1

h4': SurjVal.v valp (Model.b4 e.toModel) ofN (q + 1)

h6': SurjVal.v valp (Model.b6 e.toModel) ofN (2 * q)

h8': SurjVal.v valp (Model.b8 e.toModel) ofN (2 * q + 1)


ha.ha.ha
SurjVal.v valp (-Model.b2 e.toModel * Model.b2 e.toModel * Model.b8 e.toModel) ofN (2 * q + 3)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

hq: q > 1

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)

h2': SurjVal.v valp (Model.b2 e.toModel) ofN 1

h4': SurjVal.v valp (Model.b4 e.toModel) ofN (q + 1)

h6': SurjVal.v valp (Model.b6 e.toModel) ofN (2 * q)

h8': SurjVal.v valp (Model.b8 e.toModel) ofN (2 * q + 1)


ha.ha.ha
SurjVal.v valp (Model.b2 e.toModel * Model.b2 e.toModel * Model.b8 e.toModel) ofN (2 * q + 1 + (1 + 1))
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

hq: q > 1

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)

h2': SurjVal.v valp (Model.b2 e.toModel) ofN 1

h4': SurjVal.v valp (Model.b4 e.toModel) ofN (q + 1)

h6': SurjVal.v valp (Model.b6 e.toModel) ofN (2 * q)

h8': SurjVal.v valp (Model.b8 e.toModel) ofN (2 * q + 1)


ha.ha.ha
SurjVal.v valp (-Model.b2 e.toModel * Model.b2 e.toModel * Model.b8 e.toModel) ofN (2 * q + 3)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

hq: q > 1

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)

h2': SurjVal.v valp (Model.b2 e.toModel) ofN 1

h4': SurjVal.v valp (Model.b4 e.toModel) ofN (q + 1)

h6': SurjVal.v valp (Model.b6 e.toModel) ofN (2 * q)

h8': SurjVal.v valp (Model.b8 e.toModel) ofN (2 * q + 1)


ha.ha.ha
SurjVal.v valp (Model.b8 e.toModel * (Model.b2 e.toModel * Model.b2 e.toModel)) ofN (2 * q + 1 + (1 + 1))
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

hq: q > 1

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)

h2': SurjVal.v valp (Model.b2 e.toModel) ofN 1

h4': SurjVal.v valp (Model.b4 e.toModel) ofN (q + 1)

h6': SurjVal.v valp (Model.b6 e.toModel) ofN (2 * q)

h8': SurjVal.v valp (Model.b8 e.toModel) ofN (2 * q + 1)


ha.ha.ha
SurjVal.v valp (-Model.b2 e.toModel * Model.b2 e.toModel * Model.b8 e.toModel) ofN (2 * q + 3)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

hq: q > 1

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)

h2': SurjVal.v valp (Model.b2 e.toModel) ofN 1

h4': SurjVal.v valp (Model.b4 e.toModel) ofN (q + 1)

h6': SurjVal.v valp (Model.b6 e.toModel) ofN (2 * q)

h8': SurjVal.v valp (Model.b8 e.toModel) ofN (2 * q + 1)


ha.ha.ha
SurjVal.v valp (Model.b8 e.toModel * (Model.b2 e.toModel * Model.b2 e.toModel)) ofN (2 * q + 1) + ofN (1 + 1)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

hq: q > 1

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)

h2': SurjVal.v valp (Model.b2 e.toModel) ofN 1

h4': SurjVal.v valp (Model.b4 e.toModel) ofN (q + 1)

h6': SurjVal.v valp (Model.b6 e.toModel) ofN (2 * q)

h8': SurjVal.v valp (Model.b8 e.toModel) ofN (2 * q + 1)


ha.ha.ha
SurjVal.v valp (Model.b8 e.toModel * (Model.b2 e.toModel * Model.b2 e.toModel)) ofN (2 * q + 1) + ofN (1 + 1)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

hq: q > 1

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)

h2': SurjVal.v valp (Model.b2 e.toModel) ofN 1

h4': SurjVal.v valp (Model.b4 e.toModel) ofN (q + 1)

h6': SurjVal.v valp (Model.b6 e.toModel) ofN (2 * q)

h8': SurjVal.v valp (Model.b8 e.toModel) ofN (2 * q + 1)


ha.ha.ha
SurjVal.v valp (-Model.b2 e.toModel * Model.b2 e.toModel * Model.b8 e.toModel) ofN (2 * q + 3)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

hq: q > 1

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)

h2': SurjVal.v valp (Model.b2 e.toModel) ofN 1

h4': SurjVal.v valp (Model.b4 e.toModel) ofN (q + 1)

h6': SurjVal.v valp (Model.b6 e.toModel) ofN (2 * q)

h8': SurjVal.v valp (Model.b8 e.toModel) ofN (2 * q + 1)


ha.ha.hb
SurjVal.v valp (-(8 * Model.b4 e.toModel ^ 3)) ofN (2 * q + 3)

Goals accomplished! 🐙
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

hq: q > 1

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)

h2': SurjVal.v valp (Model.b2 e.toModel) ofN 1

h4': SurjVal.v valp (Model.b4 e.toModel) ofN (q + 1)

h6': SurjVal.v valp (Model.b6 e.toModel) ofN (2 * q)

h8': SurjVal.v valp (Model.b8 e.toModel) ofN (2 * q + 1)


ha.ha
SurjVal.v valp (-Model.b2 e.toModel * Model.b2 e.toModel * Model.b8 e.toModel + -(8 * Model.b4 e.toModel ^ 3)) ofN (2 * q + 3)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

hq: q > 1

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)

h2': SurjVal.v valp (Model.b2 e.toModel) ofN 1

h4': SurjVal.v valp (Model.b4 e.toModel) ofN (q + 1)

h6': SurjVal.v valp (Model.b6 e.toModel) ofN (2 * q)

h8': SurjVal.v valp (Model.b8 e.toModel) ofN (2 * q + 1)


ha.hb
SurjVal.v valp (-(27 * Model.b6 e.toModel * Model.b6 e.toModel)) ofN (2 * q + 3)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

hq: q > 1

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)

h2': SurjVal.v valp (Model.b2 e.toModel) ofN 1

h4': SurjVal.v valp (Model.b4 e.toModel) ofN (q + 1)

h6': SurjVal.v valp (Model.b6 e.toModel) ofN (2 * q)

h8': SurjVal.v valp (Model.b8 e.toModel) ofN (2 * q + 1)


ha.ha.hb
SurjVal.v valp (-(8 * Model.b4 e.toModel ^ 3)) ofN (2 * q + 3)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

hq: q > 1

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)

h2': SurjVal.v valp (Model.b2 e.toModel) ofN 1

h4': SurjVal.v valp (Model.b4 e.toModel) ofN (q + 1)

h6': SurjVal.v valp (Model.b6 e.toModel) ofN (2 * q)

h8': SurjVal.v valp (Model.b8 e.toModel) ofN (2 * q + 1)


ha.ha.hb
SurjVal.v valp (-(8 * Model.b4 e.toModel ^ 3)) ofN (2 * q + 3)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

hq: q > 1

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)

h2': SurjVal.v valp (Model.b2 e.toModel) ofN 1

h4': SurjVal.v valp (Model.b4 e.toModel) ofN (q + 1)

h6': SurjVal.v valp (Model.b6 e.toModel) ofN (2 * q)

h8': SurjVal.v valp (Model.b8 e.toModel) ofN (2 * q + 1)


ha.ha.hb
SurjVal.v valp (-(8 * Model.b4 e.toModel ^ 3)) ofN (2 * q + 3)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

hq: q > 1

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)

h2': SurjVal.v valp (Model.b2 e.toModel) ofN 1

h4': SurjVal.v valp (Model.b4 e.toModel) ofN (q + 1)

h6': SurjVal.v valp (Model.b6 e.toModel) ofN (2 * q)

h8': SurjVal.v valp (Model.b8 e.toModel) ofN (2 * q + 1)


ha.ha.hb
SurjVal.v valp (8 * Model.b4 e.toModel ^ 3) ofN (2 * q + 3)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

hq: q > 1

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)

h2': SurjVal.v valp (Model.b2 e.toModel) ofN 1

h4': SurjVal.v valp (Model.b4 e.toModel) ofN (q + 1)

h6': SurjVal.v valp (Model.b6 e.toModel) ofN (2 * q)

h8': SurjVal.v valp (Model.b8 e.toModel) ofN (2 * q + 1)


ha.ha.hb
SurjVal.v valp (-(8 * Model.b4 e.toModel ^ 3)) ofN (2 * q + 3)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

hq: q > 1

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)

h2': SurjVal.v valp (Model.b2 e.toModel) ofN 1

h4': SurjVal.v valp (Model.b4 e.toModel) ofN (q + 1)

h6': SurjVal.v valp (Model.b6 e.toModel) ofN (2 * q)

h8': SurjVal.v valp (Model.b8 e.toModel) ofN (2 * q + 1)


ha.ha.hb
SurjVal.v valp (8 * (Model.b4 e.toModel ^ 2 * Model.b4 e.toModel)) ofN (2 * q + 3)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

hq: q > 1

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)

h2': SurjVal.v valp (Model.b2 e.toModel) ofN 1

h4': SurjVal.v valp (Model.b4 e.toModel) ofN (q + 1)

h6': SurjVal.v valp (Model.b6 e.toModel) ofN (2 * q)

h8': SurjVal.v valp (Model.b8 e.toModel) ofN (2 * q + 1)


ha.ha.hb
SurjVal.v valp (-(8 * Model.b4 e.toModel ^ 3)) ofN (2 * q + 3)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

hq: q > 1

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)

h2': SurjVal.v valp (Model.b2 e.toModel) ofN 1

h4': SurjVal.v valp (Model.b4 e.toModel) ofN (q + 1)

h6': SurjVal.v valp (Model.b6 e.toModel) ofN (2 * q)

h8': SurjVal.v valp (Model.b8 e.toModel) ofN (2 * q + 1)


ha.ha.hb
SurjVal.v valp (8 * (Model.b4 e.toModel ^ 1 * Model.b4 e.toModel * Model.b4 e.toModel)) ofN (2 * q + 3)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

hq: q > 1

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)

h2': SurjVal.v valp (Model.b2 e.toModel) ofN 1

h4': SurjVal.v valp (Model.b4 e.toModel) ofN (q + 1)

h6': SurjVal.v valp (Model.b6 e.toModel) ofN (2 * q)

h8': SurjVal.v valp (Model.b8 e.toModel) ofN (2 * q + 1)


ha.ha.hb
SurjVal.v valp (-(8 * Model.b4 e.toModel ^ 3)) ofN (2 * q + 3)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

hq: q > 1

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)

h2': SurjVal.v valp (Model.b2 e.toModel) ofN 1

h4': SurjVal.v valp (Model.b4 e.toModel) ofN (q + 1)

h6': SurjVal.v valp (Model.b6 e.toModel) ofN (2 * q)

h8': SurjVal.v valp (Model.b8 e.toModel) ofN (2 * q + 1)


ha.ha.hb
SurjVal.v valp (8 * (Model.b4 e.toModel * Model.b4 e.toModel * Model.b4 e.toModel)) ofN (2 * q + 3)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

hq: q > 1

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)

h2': SurjVal.v valp (Model.b2 e.toModel) ofN 1

h4': SurjVal.v valp (Model.b4 e.toModel) ofN (q + 1)

h6': SurjVal.v valp (Model.b6 e.toModel) ofN (2 * q)

h8': SurjVal.v valp (Model.b8 e.toModel) ofN (2 * q + 1)


ha.ha.hb
SurjVal.v valp (-(8 * Model.b4 e.toModel ^ 3)) ofN (2 * q + 3)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

hq: q > 1

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)

h2': SurjVal.v valp (Model.b2 e.toModel) ofN 1

h4': SurjVal.v valp (Model.b4 e.toModel) ofN (q + 1)

h6': SurjVal.v valp (Model.b6 e.toModel) ofN (2 * q)

h8': SurjVal.v valp (Model.b8 e.toModel) ofN (2 * q + 1)


ha.ha.hb
SurjVal.v valp (8 * (Model.b4 e.toModel * Model.b4 e.toModel * Model.b4 e.toModel)) ofN (q + q + 3)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

hq: q > 1

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)

h2': SurjVal.v valp (Model.b2 e.toModel) ofN 1

h4': SurjVal.v valp (Model.b4 e.toModel) ofN (q + 1)

h6': SurjVal.v valp (Model.b6 e.toModel) ofN (2 * q)

h8': SurjVal.v valp (Model.b8 e.toModel) ofN (2 * q + 1)


ha.ha.hb
SurjVal.v valp (-(8 * Model.b4 e.toModel ^ 3)) ofN (2 * q + 3)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

hq: q > 1

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)

h2': SurjVal.v valp (Model.b2 e.toModel) ofN 1

h4': SurjVal.v valp (Model.b4 e.toModel) ofN (q + 1)

h6': SurjVal.v valp (Model.b6 e.toModel) ofN (2 * q)

h8': SurjVal.v valp (Model.b8 e.toModel) ofN (2 * q + 1)


ha.ha.hb
SurjVal.v valp (8 * (Model.b4 e.toModel * Model.b4 e.toModel * Model.b4 e.toModel)) ofN (q + q + 3)

Goals accomplished! 🐙
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

hq: q > 1

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)

h2': SurjVal.v valp (Model.b2 e.toModel) ofN 1

h4': SurjVal.v valp (Model.b4 e.toModel) ofN (q + 1)

h6': SurjVal.v valp (Model.b6 e.toModel) ofN (2 * q)

h8': SurjVal.v valp (Model.b8 e.toModel) ofN (2 * q + 1)


ha.ha.hb
SurjVal.v valp (8 * (Model.b4 e.toModel * Model.b4 e.toModel * Model.b4 e.toModel)) ofN (q + 1 + (q + 1) + 1)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

hq: q > 1

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)

h2': SurjVal.v valp (Model.b2 e.toModel) ofN 1

h4': SurjVal.v valp (Model.b4 e.toModel) ofN (q + 1)

h6': SurjVal.v valp (Model.b6 e.toModel) ofN (2 * q)

h8': SurjVal.v valp (Model.b8 e.toModel) ofN (2 * q + 1)


ha.ha.hb
SurjVal.v valp (-(8 * Model.b4 e.toModel ^ 3)) ofN (2 * q + 3)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

hq: q > 1

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)

h2': SurjVal.v valp (Model.b2 e.toModel) ofN 1

h4': SurjVal.v valp (Model.b4 e.toModel) ofN (q + 1)

h6': SurjVal.v valp (Model.b6 e.toModel) ofN (2 * q)

h8': SurjVal.v valp (Model.b8 e.toModel) ofN (2 * q + 1)


ha.ha.hb
SurjVal.v valp (8 * (Model.b4 e.toModel * Model.b4 e.toModel * Model.b4 e.toModel)) ofN (q + 1 + (q + 1)) + ofN 1
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

hq: q > 1

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)

h2': SurjVal.v valp (Model.b2 e.toModel) ofN 1

h4': SurjVal.v valp (Model.b4 e.toModel) ofN (q + 1)

h6': SurjVal.v valp (Model.b6 e.toModel) ofN (2 * q)

h8': SurjVal.v valp (Model.b8 e.toModel) ofN (2 * q + 1)


ha.ha.hb
SurjVal.v valp (-(8 * Model.b4 e.toModel ^ 3)) ofN (2 * q + 3)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

hq: q > 1

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)

h2': SurjVal.v valp (Model.b2 e.toModel) ofN 1

h4': SurjVal.v valp (Model.b4 e.toModel) ofN (q + 1)

h6': SurjVal.v valp (Model.b6 e.toModel) ofN (2 * q)

h8': SurjVal.v valp (Model.b8 e.toModel) ofN (2 * q + 1)


ha.ha.hb
SurjVal.v valp (8 * (Model.b4 e.toModel * Model.b4 e.toModel * Model.b4 e.toModel)) ofN (q + 1) + ofN (q + 1) + ofN 1
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

hq: q > 1

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)

h2': SurjVal.v valp (Model.b2 e.toModel) ofN 1

h4': SurjVal.v valp (Model.b4 e.toModel) ofN (q + 1)

h6': SurjVal.v valp (Model.b6 e.toModel) ofN (2 * q)

h8': SurjVal.v valp (Model.b8 e.toModel) ofN (2 * q + 1)


ha.ha.hb
SurjVal.v valp (8 * (Model.b4 e.toModel * Model.b4 e.toModel * Model.b4 e.toModel)) ofN (q + 1) + ofN (q + 1) + ofN 1
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

hq: q > 1

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)

h2': SurjVal.v valp (Model.b2 e.toModel) ofN 1

h4': SurjVal.v valp (Model.b4 e.toModel) ofN (q + 1)

h6': SurjVal.v valp (Model.b6 e.toModel) ofN (2 * q)

h8': SurjVal.v valp (Model.b8 e.toModel) ofN (2 * q + 1)


ha.ha.hb
SurjVal.v valp (-(8 * Model.b4 e.toModel ^ 3)) ofN (2 * q + 3)

Goals accomplished! 🐙
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

hq: q > 1

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)

h2': SurjVal.v valp (Model.b2 e.toModel) ofN 1

h4': SurjVal.v valp (Model.b4 e.toModel) ofN (q + 1)

h6': SurjVal.v valp (Model.b6 e.toModel) ofN (2 * q)

h8': SurjVal.v valp (Model.b8 e.toModel) ofN (2 * q + 1)


ha
SurjVal.v valp (-Model.b2 e.toModel * Model.b2 e.toModel * Model.b8 e.toModel + -(8 * Model.b4 e.toModel ^ 3) + -(27 * Model.b6 e.toModel * Model.b6 e.toModel)) ofN (2 * q + 3)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

hq: q > 1

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)

h2': SurjVal.v valp (Model.b2 e.toModel) ofN 1

h4': SurjVal.v valp (Model.b4 e.toModel) ofN (q + 1)

h6': SurjVal.v valp (Model.b6 e.toModel) ofN (2 * q)

h8': SurjVal.v valp (Model.b8 e.toModel) ofN (2 * q + 1)


hb
SurjVal.v valp (9 * Model.b2 e.toModel * Model.b4 e.toModel * Model.b6 e.toModel) ofN (2 * q + 3)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

hq: q > 1

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)

h2': SurjVal.v valp (Model.b2 e.toModel) ofN 1

h4': SurjVal.v valp (Model.b4 e.toModel) ofN (q + 1)

h6': SurjVal.v valp (Model.b6 e.toModel) ofN (2 * q)

h8': SurjVal.v valp (Model.b8 e.toModel) ofN (2 * q + 1)


ha.hb
SurjVal.v valp (-(27 * Model.b6 e.toModel * Model.b6 e.toModel)) ofN (2 * q + 3)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

hq: q > 1

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)

h2': SurjVal.v valp (Model.b2 e.toModel) ofN 1

h4': SurjVal.v valp (Model.b4 e.toModel) ofN (q + 1)

h6': SurjVal.v valp (Model.b6 e.toModel) ofN (2 * q)

h8': SurjVal.v valp (Model.b8 e.toModel) ofN (2 * q + 1)


ha.hb
SurjVal.v valp (-(27 * Model.b6 e.toModel * Model.b6 e.toModel)) ofN (2 * q + 3)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

hq: q > 1

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)

h2': SurjVal.v valp (Model.b2 e.toModel) ofN 1

h4': SurjVal.v valp (Model.b4 e.toModel) ofN (q + 1)

h6': SurjVal.v valp (Model.b6 e.toModel) ofN (2 * q)

h8': SurjVal.v valp (Model.b8 e.toModel) ofN (2 * q + 1)


ha.hb
SurjVal.v valp (-(27 * Model.b6 e.toModel * Model.b6 e.toModel)) ofN (2 * q + 3)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

hq: q > 1

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)

h2': SurjVal.v valp (Model.b2 e.toModel) ofN 1

h4': SurjVal.v valp (Model.b4 e.toModel) ofN (q + 1)

h6': SurjVal.v valp (Model.b6 e.toModel) ofN (2 * q)

h8': SurjVal.v valp (Model.b8 e.toModel) ofN (2 * q + 1)


ha.hb
SurjVal.v valp (27 * Model.b6 e.toModel * Model.b6 e.toModel) ofN (2 * q + 3)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

hq: q > 1

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)

h2': SurjVal.v valp (Model.b2 e.toModel) ofN 1

h4': SurjVal.v valp (Model.b4 e.toModel) ofN (q + 1)

h6': SurjVal.v valp (Model.b6 e.toModel) ofN (2 * q)

h8': SurjVal.v valp (Model.b8 e.toModel) ofN (2 * q + 1)


ha.hb
SurjVal.v valp (-(27 * Model.b6 e.toModel * Model.b6 e.toModel)) ofN (2 * q + 3)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

hq: q > 1

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)

h2': SurjVal.v valp (Model.b2 e.toModel) ofN 1

h4': SurjVal.v valp (Model.b4 e.toModel) ofN (q + 1)

h6': SurjVal.v valp (Model.b6 e.toModel) ofN (2 * q)

h8': SurjVal.v valp (Model.b8 e.toModel) ofN (2 * q + 1)


ha.hb
SurjVal.v valp (27 * Model.b6 e.toModel * Model.b6 e.toModel) ofN (2 * q) + ofN 3
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

hq: q > 1

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)

h2': SurjVal.v valp (Model.b2 e.toModel) ofN 1

h4': SurjVal.v valp (Model.b4 e.toModel) ofN (q + 1)

h6': SurjVal.v valp (Model.b6 e.toModel) ofN (2 * q)

h8': SurjVal.v valp (Model.b8 e.toModel) ofN (2 * q + 1)


ha.hb
SurjVal.v valp (-(27 * Model.b6 e.toModel * Model.b6 e.toModel)) ofN (2 * q + 3)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

hq: q > 1

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)

h2': SurjVal.v valp (Model.b2 e.toModel) ofN 1

h4': SurjVal.v valp (Model.b4 e.toModel) ofN (q + 1)

h6': SurjVal.v valp (Model.b6 e.toModel) ofN (2 * q)

h8': SurjVal.v valp (Model.b8 e.toModel) ofN (2 * q + 1)


ha.hb
SurjVal.v valp (27 * (Model.b6 e.toModel * Model.b6 e.toModel)) ofN (2 * q) + ofN 3
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

hq: q > 1

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)

h2': SurjVal.v valp (Model.b2 e.toModel) ofN 1

h4': SurjVal.v valp (Model.b4 e.toModel) ofN (q + 1)

h6': SurjVal.v valp (Model.b6 e.toModel) ofN (2 * q)

h8': SurjVal.v valp (Model.b8 e.toModel) ofN (2 * q + 1)


ha.hb
SurjVal.v valp (-(27 * Model.b6 e.toModel * Model.b6 e.toModel)) ofN (2 * q + 3)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

hq: q > 1

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)

h2': SurjVal.v valp (Model.b2 e.toModel) ofN 1

h4': SurjVal.v valp (Model.b4 e.toModel) ofN (q + 1)

h6': SurjVal.v valp (Model.b6 e.toModel) ofN (2 * q)

h8': SurjVal.v valp (Model.b8 e.toModel) ofN (2 * q + 1)


ha.hb
SurjVal.v valp (27 * (Model.b6 e.toModel * Model.b6 e.toModel)) ofN (2 * q) + ofN 3

Goals accomplished! 🐙
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

hq: q > 1

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)

h2': SurjVal.v valp (Model.b2 e.toModel) ofN 1

h4': SurjVal.v valp (Model.b4 e.toModel) ofN (q + 1)

h6': SurjVal.v valp (Model.b6 e.toModel) ofN (2 * q)

h8': SurjVal.v valp (Model.b8 e.toModel) ofN (2 * q + 1)


ha.hb
SurjVal.v valp (27 * (Model.b6 e.toModel * Model.b6 e.toModel)) ofN (2 * q) + ofN (2 + 1)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

hq: q > 1

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)

h2': SurjVal.v valp (Model.b2 e.toModel) ofN 1

h4': SurjVal.v valp (Model.b4 e.toModel) ofN (q + 1)

h6': SurjVal.v valp (Model.b6 e.toModel) ofN (2 * q)

h8': SurjVal.v valp (Model.b8 e.toModel) ofN (2 * q + 1)


ha.hb
SurjVal.v valp (27 * (Model.b6 e.toModel * Model.b6 e.toModel)) ofN (2 * q) + ofN (2 + 1)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

hq: q > 1

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)

h2': SurjVal.v valp (Model.b2 e.toModel) ofN 1

h4': SurjVal.v valp (Model.b4 e.toModel) ofN (q + 1)

h6': SurjVal.v valp (Model.b6 e.toModel) ofN (2 * q)

h8': SurjVal.v valp (Model.b8 e.toModel) ofN (2 * q + 1)


ha.hb
SurjVal.v valp (-(27 * Model.b6 e.toModel * Model.b6 e.toModel)) ofN (2 * q + 3)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

hq: q > 1

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)

h2': SurjVal.v valp (Model.b2 e.toModel) ofN 1

h4': SurjVal.v valp (Model.b4 e.toModel) ofN (q + 1)

h6': SurjVal.v valp (Model.b6 e.toModel) ofN (2 * q)

h8': SurjVal.v valp (Model.b8 e.toModel) ofN (2 * q + 1)


2 + 1 2 * q
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

hq: q > 1

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)

h2': SurjVal.v valp (Model.b2 e.toModel) ofN 1

h4': SurjVal.v valp (Model.b4 e.toModel) ofN (q + 1)

h6': SurjVal.v valp (Model.b6 e.toModel) ofN (2 * q)

h8': SurjVal.v valp (Model.b8 e.toModel) ofN (2 * q + 1)


ha.hb
SurjVal.v valp (-(27 * Model.b6 e.toModel * Model.b6 e.toModel)) ofN (2 * q + 3)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

hq: q > 1

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)

h2': SurjVal.v valp (Model.b2 e.toModel) ofN 1

h4': SurjVal.v valp (Model.b4 e.toModel) ofN (q + 1)

h6': SurjVal.v valp (Model.b6 e.toModel) ofN (2 * q)

h8': SurjVal.v valp (Model.b8 e.toModel) ofN (2 * q + 1)


2 + 1 2 * q
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

hq: q > 1

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)

h2': SurjVal.v valp (Model.b2 e.toModel) ofN 1

h4': SurjVal.v valp (Model.b4 e.toModel) ofN (q + 1)

h6': SurjVal.v valp (Model.b6 e.toModel) ofN (2 * q)

h8': SurjVal.v valp (Model.b8 e.toModel) ofN (2 * q + 1)


2 + 1 q + q
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

hq: q > 1

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)

h2': SurjVal.v valp (Model.b2 e.toModel) ofN 1

h4': SurjVal.v valp (Model.b4 e.toModel) ofN (q + 1)

h6': SurjVal.v valp (Model.b6 e.toModel) ofN (2 * q)

h8': SurjVal.v valp (Model.b8 e.toModel) ofN (2 * q + 1)


2 + 1 q + q
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

hq: q > 1

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)

h2': SurjVal.v valp (Model.b2 e.toModel) ofN 1

h4': SurjVal.v valp (Model.b4 e.toModel) ofN (q + 1)

h6': SurjVal.v valp (Model.b6 e.toModel) ofN (2 * q)

h8': SurjVal.v valp (Model.b8 e.toModel) ofN (2 * q + 1)


ha.hb
SurjVal.v valp (-(27 * Model.b6 e.toModel * Model.b6 e.toModel)) ofN (2 * q + 3)

Goals accomplished! 🐙
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

hq: q > 1

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)


SurjVal.v valp (Model.discr e.toModel) ofN (2 * q + 3)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

hq: q > 1

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)

h2': SurjVal.v valp (Model.b2 e.toModel) ofN 1

h4': SurjVal.v valp (Model.b4 e.toModel) ofN (q + 1)

h6': SurjVal.v valp (Model.b6 e.toModel) ofN (2 * q)

h8': SurjVal.v valp (Model.b8 e.toModel) ofN (2 * q + 1)


hb
SurjVal.v valp (9 * Model.b2 e.toModel * Model.b4 e.toModel * Model.b6 e.toModel) ofN (2 * q + 3)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

hq: q > 1

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)

h2': SurjVal.v valp (Model.b2 e.toModel) ofN 1

h4': SurjVal.v valp (Model.b4 e.toModel) ofN (q + 1)

h6': SurjVal.v valp (Model.b6 e.toModel) ofN (2 * q)

h8': SurjVal.v valp (Model.b8 e.toModel) ofN (2 * q + 1)


hb
SurjVal.v valp (9 * Model.b2 e.toModel * Model.b4 e.toModel * Model.b6 e.toModel) ofN (2 * q + 3)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

hq: q > 1

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)

h2': SurjVal.v valp (Model.b2 e.toModel) ofN 1

h4': SurjVal.v valp (Model.b4 e.toModel) ofN (q + 1)

h6': SurjVal.v valp (Model.b6 e.toModel) ofN (2 * q)

h8': SurjVal.v valp (Model.b8 e.toModel) ofN (2 * q + 1)


hb
SurjVal.v valp (9 * Model.b2 e.toModel * Model.b4 e.toModel * Model.b6 e.toModel) ofN (2 * q + 3)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

hq: q > 1

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)

h2': SurjVal.v valp (Model.b2 e.toModel) ofN 1

h4': SurjVal.v valp (Model.b4 e.toModel) ofN (q + 1)

h6': SurjVal.v valp (Model.b6 e.toModel) ofN (2 * q)

h8': SurjVal.v valp (Model.b8 e.toModel) ofN (2 * q + 1)


hb
SurjVal.v valp (9 * Model.b2 e.toModel * Model.b4 e.toModel * Model.b6 e.toModel) ofN (2 * q + 3)

Goals accomplished! 🐙
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

hq: q > 1

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)

h2': SurjVal.v valp (Model.b2 e.toModel) ofN 1

h4': SurjVal.v valp (Model.b4 e.toModel) ofN (q + 1)

h6': SurjVal.v valp (Model.b6 e.toModel) ofN (2 * q)

h8': SurjVal.v valp (Model.b8 e.toModel) ofN (2 * q + 1)


hb
SurjVal.v valp (9 * Model.b2 e.toModel * Model.b4 e.toModel * Model.b6 e.toModel) ofN (2 * q + (1 + (1 + 1)))
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

hq: q > 1

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)

h2': SurjVal.v valp (Model.b2 e.toModel) ofN 1

h4': SurjVal.v valp (Model.b4 e.toModel) ofN (q + 1)

h6': SurjVal.v valp (Model.b6 e.toModel) ofN (2 * q)

h8': SurjVal.v valp (Model.b8 e.toModel) ofN (2 * q + 1)


hb
SurjVal.v valp (9 * Model.b2 e.toModel * Model.b4 e.toModel * Model.b6 e.toModel) ofN (2 * q + 3)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

hq: q > 1

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)

h2': SurjVal.v valp (Model.b2 e.toModel) ofN 1

h4': SurjVal.v valp (Model.b4 e.toModel) ofN (q + 1)

h6': SurjVal.v valp (Model.b6 e.toModel) ofN (2 * q)

h8': SurjVal.v valp (Model.b8 e.toModel) ofN (2 * q + 1)


hb
SurjVal.v valp (9 * Model.b2 e.toModel * Model.b4 e.toModel * Model.b6 e.toModel) ofN (2 * q) + ofN (1 + (1 + 1))
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

hq: q > 1

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)

h2': SurjVal.v valp (Model.b2 e.toModel) ofN 1

h4': SurjVal.v valp (Model.b4 e.toModel) ofN (q + 1)

h6': SurjVal.v valp (Model.b6 e.toModel) ofN (2 * q)

h8': SurjVal.v valp (Model.b8 e.toModel) ofN (2 * q + 1)


hb
SurjVal.v valp (9 * Model.b2 e.toModel * Model.b4 e.toModel * Model.b6 e.toModel) ofN (2 * q + 3)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

hq: q > 1

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)

h2': SurjVal.v valp (Model.b2 e.toModel) ofN 1

h4': SurjVal.v valp (Model.b4 e.toModel) ofN (q + 1)

h6': SurjVal.v valp (Model.b6 e.toModel) ofN (2 * q)

h8': SurjVal.v valp (Model.b8 e.toModel) ofN (2 * q + 1)


hb
SurjVal.v valp (9 * Model.b2 e.toModel * Model.b4 e.toModel * Model.b6 e.toModel) ofN (2 * q) + (ofN 1 + ofN (1 + 1))
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

hq: q > 1

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)

h2': SurjVal.v valp (Model.b2 e.toModel) ofN 1

h4': SurjVal.v valp (Model.b4 e.toModel) ofN (q + 1)

h6': SurjVal.v valp (Model.b6 e.toModel) ofN (2 * q)

h8': SurjVal.v valp (Model.b8 e.toModel) ofN (2 * q + 1)


hb
SurjVal.v valp (9 * Model.b2 e.toModel * Model.b4 e.toModel * Model.b6 e.toModel) ofN (2 * q + 3)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

hq: q > 1

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)

h2': SurjVal.v valp (Model.b2 e.toModel) ofN 1

h4': SurjVal.v valp (Model.b4 e.toModel) ofN (q + 1)

h6': SurjVal.v valp (Model.b6 e.toModel) ofN (2 * q)

h8': SurjVal.v valp (Model.b8 e.toModel) ofN (2 * q + 1)


hb
SurjVal.v valp (Model.b6 e.toModel * (9 * Model.b2 e.toModel * Model.b4 e.toModel)) ofN (2 * q) + (ofN 1 + ofN (1 + 1))
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

hq: q > 1

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)

h2': SurjVal.v valp (Model.b2 e.toModel) ofN 1

h4': SurjVal.v valp (Model.b4 e.toModel) ofN (q + 1)

h6': SurjVal.v valp (Model.b6 e.toModel) ofN (2 * q)

h8': SurjVal.v valp (Model.b8 e.toModel) ofN (2 * q + 1)


hb
SurjVal.v valp (9 * Model.b2 e.toModel * Model.b4 e.toModel * Model.b6 e.toModel) ofN (2 * q + 3)
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

hq: q > 1

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)

h2': SurjVal.v valp (Model.b2 e.toModel) ofN 1

h4': SurjVal.v valp (Model.b4 e.toModel) ofN (q + 1)

h6': SurjVal.v valp (Model.b6 e.toModel) ofN (2 * q)

h8': SurjVal.v valp (Model.b8 e.toModel) ofN (2 * q + 1)


hb
SurjVal.v valp (Model.b6 e.toModel * (9 * (Model.b2 e.toModel * Model.b4 e.toModel))) ofN (2 * q) + (ofN 1 + ofN (1 + 1))
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

hq: q > 1

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)

h2': SurjVal.v valp (Model.b2 e.toModel) ofN 1

h4': SurjVal.v valp (Model.b4 e.toModel) ofN (q + 1)

h6': SurjVal.v valp (Model.b6 e.toModel) ofN (2 * q)

h8': SurjVal.v valp (Model.b8 e.toModel) ofN (2 * q + 1)


hb
SurjVal.v valp (Model.b6 e.toModel * (9 * (Model.b2 e.toModel * Model.b4 e.toModel))) ofN (2 * q) + (ofN 1 + ofN (1 + 1))
R: Type u

inst: IntegralDomain R

q:

p: R

valp: SurjVal p

e: ValidModel R

hq: q > 1

h1: SurjVal.v valp e.toModel.a1 ofN 1

h2: SurjVal.v valp e.toModel.a2 = ofN 1

h3: SurjVal.v valp e.toModel.a3 ofN q

h4: SurjVal.v valp e.toModel.a4 ofN (q + 1)

h6: SurjVal.v valp e.toModel.a6 ofN (2 * q)

h2': SurjVal.v valp (Model.b2 e.toModel) ofN 1

h4': SurjVal.v valp (Model.b4 e.toModel) ofN (q + 1)

h6': SurjVal.v valp (Model.b6 e.toModel) ofN (2 * q)

h8': SurjVal.v valp (Model.b8 e.toModel) ofN (2 * q + 1)


hb
SurjVal.v valp (9 * Model.b2 e.toModel * Model.b4 e.toModel * Model.b6 e.toModel) ofN (2 * q + 3)

Goals accomplished! 🐙
lemma
small_char_div_12: ∀ {p : R}, p = 2 p = 3∀ (valp : SurjVal p), SurjVal.v valp 12 ofN 1
small_char_div_12
{
p: R
p
:
R: Type u
R
} (
hp: p = 2 p = 3
hp
:
p: R
p
=
2: ?m.26517
2
p: R
p
=
3: ?m.26583
3
) (
valp: SurjVal p
valp
:
SurjVal: {R : Type ?u.26627} → R[inst : IntegralDomain R] → Type ?u.26627
SurjVal
p: R
p
) :
valp: SurjVal p
valp
.
v: {R : Type ?u.26634} → {p : R} → [inst : IntegralDomain R] → SurjVal pRℕ∪∞
v
12: ?m.26642
12
ofN: ℕ∪∞
ofN
1: ?m.26673
1
:=
R: Type u

inst: IntegralDomain R

p: R

hp: p = 2 p = 3

valp: SurjVal p


SurjVal.v valp 12 ofN 1
R: Type u

inst: IntegralDomain R

p: R

hp: p = 2 p = 3

valp: SurjVal p


SurjVal.v valp 12 ofN 1
R: Type u

inst: IntegralDomain R

p: R

valp: SurjVal p

p2: p = 2


inl
SurjVal.v valp 12 ofN 1
R: Type u

inst: IntegralDomain R

p: R

valp: SurjVal p

p2: p = 2


inl
SurjVal.v valp 12 ofN 1
R: Type u

inst: IntegralDomain R

p: R

valp: SurjVal p

p2: p = 2


inl
SurjVal.v valp 12 ofN 1

Goals accomplished! 🐙
R: Type u

inst: IntegralDomain R

p: R

valp: SurjVal p

p2: p = 2


inl
SurjVal.v valp (2 * 6) ofN 1
R: Type u

inst: IntegralDomain R

p: R

valp: SurjVal p

p2: p = 2


inl
SurjVal.v valp (2 * 6) ofN 1
R: Type u

inst: IntegralDomain R

p: R

valp: SurjVal p

p2: p = 2


inl
SurjVal.v valp 12 ofN 1
R: Type u

inst: IntegralDomain R

p: R

valp: SurjVal p

p2: p = 2


inl.ha
SurjVal.v valp 2 ofN 1
R: Type u

inst: IntegralDomain R

p: R

valp: SurjVal p

p2: p = 2


inl
SurjVal.v valp 12 ofN 1
R: Type u

inst: IntegralDomain R

p: R

valp: SurjVal p

p2: p = 2


inl.ha
SurjVal.v valp 2 ofN 1
R: Type u

inst: IntegralDomain R

p: R

valp: SurjVal p

p2: p = 2


inl.ha
SurjVal.v valp p ofN 1
R: Type u

inst: IntegralDomain R

p: R

valp: SurjVal p

p2: p = 2


inl.ha
SurjVal.v valp p ofN 1
R: Type u

inst: IntegralDomain R

p: R

valp: SurjVal p

p2: p = 2


inl
SurjVal.v valp 12 ofN 1

Goals accomplished! 🐙
R: Type u

inst: IntegralDomain R

p: R

hp: p = 2 p = 3

valp: SurjVal p


SurjVal.v valp 12 ofN 1
R: Type u

inst: IntegralDomain R

p: R

valp: SurjVal p

p3: p = 3


inr
SurjVal.v valp 12 ofN 1
R: Type u

inst: IntegralDomain R

p: R

valp: SurjVal p

p3: p = 3


inr
SurjVal.v valp 12 ofN 1
R: Type u

inst: IntegralDomain R

p: R

valp: SurjVal p

p3: p = 3


inr
SurjVal.v valp 12 ofN 1

Goals accomplished! 🐙
R: Type u

inst: IntegralDomain R

p: R

valp: SurjVal p

p3: p = 3


inr
SurjVal.v valp (3 * 4) ofN 1
R: Type u

inst: IntegralDomain R

p: R

valp: SurjVal p

p3: p = 3


inr
SurjVal.v valp (3 * 4) ofN 1
R: Type u

inst: IntegralDomain R

p: R

valp: SurjVal p

p3: p = 3


inr
SurjVal.v valp 12 ofN 1
R: Type u

inst: IntegralDomain R

p: R

valp: SurjVal p

p3: p = 3


inr.ha
SurjVal.v valp 3 ofN 1
R: Type u

inst: IntegralDomain R

p: R

valp: SurjVal p

p3: p = 3


inr
SurjVal.v valp 12 ofN 1
R: Type u

inst: IntegralDomain R

p: R

valp: SurjVal p

p3: p = 3


inr.ha
SurjVal.v valp 3 ofN 1
R: Type u

inst: IntegralDomain R

p: R

valp: SurjVal p

p3: p = 3


inr.ha
SurjVal.v valp p ofN 1
R: Type u

inst: IntegralDomain R

p: R

valp: SurjVal p

p3: p = 3


inr.ha
SurjVal.v valp p ofN 1
R: Type u

inst: IntegralDomain R

p: R

valp: SurjVal p

p3: p = 3


inr
SurjVal.v valp 12 ofN 1

Goals accomplished! 🐙
lemma
v_rst_b2_of_small_char: ∀ {R : Type u} [inst : IntegralDomain R] {p : R} (valp : SurjVal p) (e : ValidModel R) (r s t : R), SurjVal.v valp (Model.b2 e.toModel) ofN 1SurjVal.v valp 12 ofN 1SurjVal.v valp (Model.b2 (rst_iso r s t e).toModel) ofN 1
v_rst_b2_of_small_char
{
p: R
p
:
R: Type u
R
} (
valp: SurjVal p
valp
:
SurjVal: {R : Type ?u.27282} → R[inst : IntegralDomain R] → Type ?u.27282
SurjVal
p: R
p
) (e :
ValidModel: (R : Type ?u.27290) → [inst : IntegralDomain R] → Type ?u.27290
ValidModel
R: Type u
R
) (
r: R
r
s: R
s
t: R
t
:
R: Type u
R
) (
h_b2: SurjVal.v valp (Model.b2 e.toModel) ofN 1
h_b2
:
valp: SurjVal p
valp
.
v: {R : Type ?u.27301} → {p : R} → [inst : IntegralDomain R] → SurjVal pRℕ∪∞
v
e.
b2: {R : Type ?u.27313} → [inst : IntegralDomain R] → Model RR
b2
ofN: ℕ∪∞
ofN
1: ?m.27322
1
) (
h_p: SurjVal.v valp 12 ofN 1
h_p
:
valp: SurjVal p
valp
.
v: {R : Type ?u.27340} → {p : R} → [inst : IntegralDomain R] → SurjVal pRℕ∪∞
v
12: ?m.27345
12
ofN: ℕ∪∞
ofN
1: ?m.27396
1
) :
valp: SurjVal p
valp
.
v: {R : Type ?u.27403} → {p : R} → [inst : IntegralDomain R] → SurjVal pRℕ∪∞
v
(
rst_iso: {R : Type ?u.27407} → [inst : IntegralDomain R] → RRRValidModel RValidModel R
rst_iso
r: R
r
s: R
s
t: R
t
e).
b2: {R : Type ?u.27413} → [inst : IntegralDomain R] → Model RR
b2
ofN: ℕ∪∞
ofN
1: ?m.27420
1
:=
R: Type u

inst: IntegralDomain R

p: R

valp: SurjVal p

e: ValidModel R

r, s, t: R

h_b2: SurjVal.v valp (Model.b2 e.toModel) ofN 1

h_p: SurjVal.v valp 12 ofN 1


SurjVal.v valp (Model.b2 (rst_iso r s t e).toModel) ofN 1
R: Type u

inst: IntegralDomain R

p: R

valp: SurjVal p

e: ValidModel R

r, s, t: R

h_b2: SurjVal.v valp (Model.b2 e.toModel) ofN 1

h_p: SurjVal.v valp 12 ofN 1


SurjVal.v valp (Model.b2 (Model.rst_iso r s t e.toModel)) ofN 1
R: Type u

inst: IntegralDomain R

p: R

valp: SurjVal p

e: ValidModel R

r, s, t: R

h_b2: SurjVal.v valp (Model.b2 e.toModel) ofN 1

h_p: SurjVal.v valp 12 ofN 1


SurjVal.v valp (Model.b2 (rst_iso r s t e).toModel) ofN 1
R: Type u

inst: IntegralDomain R

p: R

valp: SurjVal p

e: ValidModel R

r, s, t: R

h_b2: SurjVal.v valp (Model.b2 e.toModel) ofN 1

h_p: SurjVal.v valp 12 ofN 1


SurjVal.v valp (Model.b2 (Model.rst_iso r s t e.toModel)) ofN 1
R: Type u

inst: IntegralDomain R

p: R

valp: SurjVal p

e: ValidModel R

r, s, t: R

h_b2: SurjVal.v valp (Model.b2 e.toModel) ofN 1

h_p: SurjVal.v valp 12 ofN 1


SurjVal.v valp (Model.b2 e.toModel + 12 * r) ofN 1
R: Type u

inst: IntegralDomain R

p: R

valp: SurjVal p

e: ValidModel R

r, s, t: R

h_b2: SurjVal.v valp (Model.b2 e.toModel) ofN 1

h_p: SurjVal.v valp 12 ofN 1


SurjVal.v valp (Model.b2 e.toModel + 12 * r) ofN 1
R: Type u

inst: IntegralDomain R

p: R

valp: SurjVal p

e: ValidModel R

r, s, t: R

h_b2: SurjVal.v valp (Model.b2 e.toModel) ofN 1

h_p: SurjVal.v valp 12 ofN 1


SurjVal.v valp (Model.b2 (rst_iso r s t e).toModel) ofN 1
R: Type u

inst: IntegralDomain R

p: R

valp: SurjVal p

e: ValidModel R

r, s, t: R

h_b2: SurjVal.v valp (Model.b2 e.toModel) ofN 1

h_p: SurjVal.v valp 12 ofN 1


SurjVal.v valp (12 * r) ofN 1
R: Type u

inst: IntegralDomain R

p: R

valp: SurjVal p

e: ValidModel R

r, s, t: R

h_b2: SurjVal.v valp (Model.b2 e.toModel) ofN 1

h_p: SurjVal.v valp 12 ofN 1


SurjVal.v valp (Model.b2 (rst_iso r s t e).toModel) ofN 1

Goals accomplished! 🐙
section cubic def
Δcubic: {R : Type u} → [inst : IntegralDomain R] → R × R × RR
Δcubic
(
c: R × R × R
c
:
R: Type u
R
×
R: Type u
R
×
R: Type u
R
) :
R: Type u
R
:=
18: ?m.27661
18
*
c: R × R × R
c
.
1: {α : Type ?u.27671} → {β : Type ?u.27670} → α × βα
1
*
c: R × R × R
c
.
2: {α : Type ?u.27677} → {β : Type ?u.27676} → α × ββ
2
.
1: {α : Type ?u.27681} → {β : Type ?u.27680} → α × βα
1
*
c: R × R × R
c
.
2: {α : Type ?u.27685} → {β : Type ?u.27684} → α × ββ
2
.
2: {α : Type ?u.27689} → {β : Type ?u.27688} → α × ββ
2
-
4: ?m.27699
4
*
c: R × R × R
c
.
1: {α : Type ?u.27712} → {β : Type ?u.27711} → α × βα
1
^
3: ?m.27716
3
*
c: R × R × R
c
.
2: {α : Type ?u.27726} → {β : Type ?u.27725} → α × ββ
2
.
2: {α : Type ?u.27730} → {β : Type ?u.27729} → α × ββ
2
+
c: R × R × R
c
.
1: {α : Type ?u.27740} → {β : Type ?u.27739} → α × βα
1
^
2: ?m.27744
2
*
c: R × R × R
c
.
2: {α : Type ?u.27757} → {β : Type ?u.27756} → α × ββ
2
.
1: {α : Type ?u.27761} → {β : Type ?u.27760} → α × βα
1
^
2: ?m.27765
2
-
4: ?m.27778
4
*
c: R × R × R
c
.
2: {α : Type ?u.27791} → {β : Type ?u.27790} → α × ββ
2
.
1: {α : Type ?u.27795} → {β : Type ?u.27794} → α × βα
1
^
3: ?m.27799
3
-
27: ?m.27812
27
*
c: R × R × R
c
.
2: {α : Type ?u.27825} → {β : Type ?u.27824} → α × ββ
2
.
2: {α : Type ?u.27829} → {β : Type ?u.27828} → α × ββ
2
^
2: ?m.27833
2
def
model_to_cubic: {p : R} → EnatValRing pValidModel RR × R × R
model_to_cubic
{
p: R
p
:
R: Type u
R
} (evr :
EnatValRing: {R : Type ?u.30568} → R[inst : IntegralDomain R] → Type ?u.30568
EnatValRing
p: R
p
) (e :
ValidModel: (R : Type ?u.30576) → [inst : IntegralDomain R] → Type ?u.30576
ValidModel
R: Type u
R
) :
R: Type u
R
×
R: Type u
R
×
R: Type u
R
:= (evr.
sub_val: {R : Type ?u.30594} → [inst : IntegralDomain R] → {p : R} → EnatValRing pRR
sub_val
e.
a2: {R : Type ?u.30612} → [inst : IntegralDomain R] → Model RR
a2
1: ?m.30618
1
, evr.
sub_val: {R : Type ?u.30632} → [inst : IntegralDomain R] → {p : R} → EnatValRing pRR
sub_val
e.
a4: {R : Type ?u.30645} → [inst : IntegralDomain R] → Model RR
a4
2: ?m.30649
2
, evr.
sub_val: {R : Type ?u.30654} → [inst : IntegralDomain R] → {p : R} → EnatValRing pRR
sub_val
e.
a6: {R : Type ?u.30667} → [inst : IntegralDomain R] → Model RR
a6
3: ?m.30671
3
) def
cubic_has_dinstinct_roots: {p : R} → EnatValRing pValidModel RProp
cubic_has_dinstinct_roots
{
p: R
p
:
R: Type u
R
} (evr :
EnatValRing: {R : Type ?u.30746} → R[inst : IntegralDomain R] → Type ?u.30746
EnatValRing
p: R
p
) (e :
ValidModel: (R : Type ?u.30754) → [inst : IntegralDomain R] → Type ?u.30754
ValidModel
R: Type u
R
) :
Prop: Type
Prop
:= evr.
valtn: {R : Type ?u.30763} → {p : R} → [inst : IntegralDomain R] → EnatValRing pSurjVal p
valtn
.
v: {R : Type ?u.30770} → {p : R} → [inst : IntegralDomain R] → SurjVal pRℕ∪∞
v
(
Δcubic: {R : Type ?u.30777} → [inst : IntegralDomain R] → R × R × RR
Δcubic
(
model_to_cubic: {R : Type ?u.30780} → [inst : IntegralDomain R] → {p : R} → EnatValRing pValidModel RR × R × R
model_to_cubic
evr e)) =
0: ?m.30789
0
def
δmultiplicity: R × R × RR
δmultiplicity
(
c: R × R × R
c
:
R: Type u
R
×
R: Type u
R
×
R: Type u
R
) :
R: Type u
R
:=
3: ?m.31054
3
*
c: R × R × R
c
.
2: {α : Type ?u.31064} → {β : Type ?u.31063} → α × ββ
2
.
1: {α : Type ?u.31070} → {β : Type ?u.31069} → α × βα
1
-
c: R × R × R
c
.
1: {α : Type ?u.31077} → {β : Type ?u.31076} → α × βα
1
^
2: ?m.31081
2
def
cubic_has_double_root: {p : R} → EnatValRing pValidModel RProp
cubic_has_double_root
{
p: R
p
:
R: Type u
R
} (evr :
EnatValRing: {R : Type ?u.31596} → R[inst : IntegralDomain R] → Type ?u.31596
EnatValRing
p: R
p
) (e :
ValidModel: (R : Type ?u.31604) → [inst : IntegralDomain R] → Type ?u.31604
ValidModel
R: Type u
R
) :
Prop: Type
Prop
:= evr.
valtn: {R : Type ?u.31613} → {p : R} → [inst : IntegralDomain R] → EnatValRing pSurjVal p
valtn
.
v: {R : Type ?u.31620} → {p : R} → [inst : IntegralDomain R] → SurjVal pRℕ∪∞
v
(
Δcubic: {R : Type ?u.31627} → [inst : IntegralDomain R] → R × R × RR
Δcubic
(
model_to_cubic: {R : Type ?u.31630} → [inst : IntegralDomain R] → {p : R} → EnatValRing pValidModel RR × R × R
model_to_cubic
evr e)) >
0: ?m.31639
0
evr.
valtn: {R : Type ?u.31878} → {p : R} → [inst : IntegralDomain R] → EnatValRing pSurjVal p
valtn
.
v: {R : Type ?u.31882} → {p : R} → [inst : IntegralDomain R] → SurjVal pRℕ∪∞
v
(
δmultiplicity: {R : Type ?u.31886} → [inst : IntegralDomain R] → R × R × RR
δmultiplicity
(
model_to_cubic: {R : Type ?u.31889} → [inst : IntegralDomain R] → {p : R} → EnatValRing pValidModel RR × R × R
model_to_cubic
evr e)) =
0: ?m.31894
0
def
cubic_has_triple_root: {p : R} → EnatValRing pValidModel RProp
cubic_has_triple_root
{
p: R
p
:
R: Type u
R
} (evr :
EnatValRing: {R : Type ?u.31928} → R[inst : IntegralDomain R] → Type ?u.31928
EnatValRing
p: R
p
) (e :
ValidModel: (R : Type ?u.31936) → [inst : IntegralDomain R] → Type ?u.31936
ValidModel
R: Type u
R
) :
Prop: Type
Prop
:= evr.
valtn: {R : Type ?u.31945} → {p : R} → [inst : IntegralDomain R] → EnatValRing pSurjVal p
valtn
.
v: {R : Type ?u.31952} → {p : R} → [inst : IntegralDomain R] → SurjVal pRℕ∪∞
v
(
Δcubic: {R : Type ?u.31959} → [inst : IntegralDomain R] → R × R × RR
Δcubic
(
model_to_cubic: {R : Type ?u.31962} → [inst : IntegralDomain R] → {p : R} → EnatValRing pValidModel RR × R × R
model_to_cubic
evr e)) >
0: ?m.31971
0
evr.
valtn: {R : Type ?u.32210} → {p : R} → [inst : IntegralDomain R] → EnatValRing pSurjVal p
valtn
.
v: {R : Type ?u.32214} → {p : R} → [inst : IntegralDomain R] → SurjVal pRℕ∪∞
v
(
δmultiplicity: {R : Type ?u.32218} → [inst : IntegralDomain R] → R × R × RR
δmultiplicity
(
model_to_cubic: {R : Type ?u.32221} → [inst : IntegralDomain R] → {p : R} → EnatValRing pValidModel RR × R × R
model_to_cubic
evr e)) >
0: ?m.32226
0
def
move_cubic_double_root_to_origin_iso: {p : R} → EnatValRing pValidModel RValidModel R
move_cubic_double_root_to_origin_iso
{
p: R
p
:
R: Type u
R
} (evr :
EnatValRing: {R : Type ?u.32261} → R[inst : IntegralDomain R] → Type ?u.32261
EnatValRing
p: R
p
) (e :
ValidModel: (R : Type ?u.32269) → [inst : IntegralDomain R] → Type ?u.32269
ValidModel
R: Type u
R
) :
ValidModel: (R : Type ?u.32273) → [inst : IntegralDomain R] → Type ?u.32273
ValidModel
R: Type u
R
:= let (
a2p: R
a2p
,
a4p2: R
a4p2
,
Warning: unused variable `a6p3` [linter.unusedVariables]
) :=
model_to_cubic: {R : Type ?u.32279} → [inst : IntegralDomain R] → {p : R} → EnatValRing pValidModel RR × R × R
model_to_cubic
evr e
rst_iso: {R : Type ?u.32336} → [inst : IntegralDomain R] → RRRValidModel RValidModel R
rst_iso
(
p: R
p
* (evr.
norm_repr: {R : Type ?u.32342} → {p : R} → [inst : IntegralDomain R] → EnatValRing pRR
norm_repr
(if evr.
residue_char: {R : Type ?u.32347} → {p : R} → [inst : IntegralDomain R] → EnatValRing p
residue_char
=
2: ?m.32352
2
then
a4p2: R
a4p2
else
a2p: R
a2p
*
a4p2: R
a4p2
)))
0: ?m.32523
0
0: ?m.32568
0
e def
cubic_double_root_is_zero: {p : R} → EnatValRing pValidModel RProp
cubic_double_root_is_zero
{
p: R
p
:
R: Type u
R
} (evr :
EnatValRing: {R : Type ?u.32904} → R[inst : IntegralDomain R] → Type ?u.32904
EnatValRing
p: R
p
) (e :
ValidModel: (R : Type ?u.32912) → [inst : IntegralDomain R] → Type ?u.32912
ValidModel
R: Type u
R
) :
Prop: Type
Prop
:= let (
a2p: R
a2p
,
a4p2: R
a4p2
,
a6p3: R
a6p3
) :=
model_to_cubic: {R : Type ?u.32920} → [inst : IntegralDomain R] → {p : R} → EnatValRing pValidModel RR × R × R
model_to_cubic
evr e evr.
valtn: {R : Type ?u.32977} → {p : R} → [inst : IntegralDomain R] → EnatValRing pSurjVal p
valtn
.
v: {R : Type ?u.32981} → {p : R} → [inst : IntegralDomain R] → SurjVal pRℕ∪∞
v
a2p: R
a2p
=
0: ?m.32989
0
evr.
valtn: {R : Type ?u.33224} → {p : R} → [inst : IntegralDomain R] → EnatValRing pSurjVal p
valtn
.
v: {R : Type ?u.33228} → {p : R} → [inst : IntegralDomain R] → SurjVal pRℕ∪∞
v
a4p2: R
a4p2
>
0: ?m.33233
0
evr.
valtn: {R : Type ?u.33254} → {p : R} → [inst : IntegralDomain R] → EnatValRing pSurjVal p
valtn
.
v: {R : Type ?u.33258} → {p : R} → [inst : IntegralDomain R] → SurjVal pRℕ∪∞
v
a6p3: R
a6p3
>
0: ?m.33263
0
lemma
Warning: declaration uses 'sorry'
{
p: R
p
:
R: Type u
R
} (evr :
EnatValRing: {R : Type ?u.33389} → R[inst : IntegralDomain R] → Type ?u.33389
EnatValRing
p: R
p
) (e :
ValidModel: (R : Type ?u.33397) → [inst : IntegralDomain R] → Type ?u.33397
ValidModel
R: Type u
R
) :
cubic_has_double_root: {R : Type ?u.33402} → [inst : IntegralDomain R] → {p : R} → EnatValRing pValidModel RProp
cubic_has_double_root
evr e
cubic_double_root_is_zero: {R : Type ?u.33415} → [inst : IntegralDomain R] → {p : R} → EnatValRing pValidModel RProp
cubic_double_root_is_zero
evr (
move_cubic_double_root_to_origin_iso: {R : Type ?u.33422} → [inst : IntegralDomain R] → {p : R} → EnatValRing pValidModel RValidModel R
move_cubic_double_root_to_origin_iso
evr e) :=
sorry: ?m.33435
sorry
def
move_cubic_triple_root_to_origin_iso: {p : R} → EnatValRing pValidModel RValidModel R
move_cubic_triple_root_to_origin_iso
{
p: R
p
:
R: Type u
R
} (evr :
EnatValRing: {R : Type ?u.33457} → R[inst : IntegralDomain R] → Type ?u.33457
EnatValRing
p: R
p
) (e :
ValidModel: (R : Type ?u.33465) → [inst : IntegralDomain R] → Type ?u.33465
ValidModel
R: Type u
R
) :
ValidModel: (R : Type ?u.33469) → [inst : IntegralDomain R] → Type ?u.33469
ValidModel
R: Type u
R
:= let (
a2p: R
a2p
,
Warning: unused variable `a4p2` [linter.unusedVariables]
,
a6p3: R
a6p3
) :=
model_to_cubic: {R : Type ?u.33475} → [inst : IntegralDomain R] → {p : R} → EnatValRing pValidModel RR × R × R
model_to_cubic
evr e
rst_iso: {R : Type ?u.33532} → [inst : IntegralDomain R] → RRRValidModel RValidModel R
rst_iso
(
p: R
p
* (evr.
norm_repr: {R : Type ?u.33538} → {p : R} → [inst : IntegralDomain R] → EnatValRing pRR
norm_repr
(if evr.
residue_char: {R : Type ?u.33543} → {p : R} → [inst : IntegralDomain R] → EnatValRing p
residue_char
=
2: ?m.33548
2
then -
a2p: R
a2p
else -
a6p3: R
a6p3
)))
0: ?m.33696
0
0: ?m.33741
0
e def
cubic_triple_root_is_zero: {p : R} → EnatValRing pValidModel RProp
cubic_triple_root_is_zero
{
p: R
p
:
R: Type u
R
} (evr :
EnatValRing: {R : Type ?u.34055} → R[inst : IntegralDomain R] → Type ?u.34055
EnatValRing
p: R
p
) (e :
ValidModel: (R : Type ?u.34063) → [inst : IntegralDomain R] → Type ?u.34063
ValidModel
R: Type u
R
) :
Prop: Type
Prop
:= let (
a2p: R
a2p
,
a4p2: R
a4p2
,
a6p3: R
a6p3
) :=
model_to_cubic: {R : Type ?u.34071} → [inst : IntegralDomain R] → {p : R} → EnatValRing pValidModel RR × R × R
model_to_cubic
evr e evr.
valtn: {R : Type ?u.34128} → {p : R} → [inst : IntegralDomain R] → EnatValRing pSurjVal p
valtn
.
v: {R : Type ?u.34132} → {p : R} → [inst : IntegralDomain R] → SurjVal pRℕ∪∞
v
a2p: R
a2p
>
0: ?m.34140
0
evr.
valtn: {R : Type ?u.34379} → {p : R} → [inst : IntegralDomain R] → EnatValRing pSurjVal p
valtn
.
v: {R : Type ?u.34383} → {p : R} → [inst : IntegralDomain R] → SurjVal pRℕ∪∞
v
a4p2: R
a4p2
>
0: ?m.34388
0
evr.
valtn: {R : Type ?u.34406} → {p : R} → [inst : IntegralDomain R] → EnatValRing pSurjVal p
valtn
.
v: {R : Type ?u.34410} → {p : R} → [inst : IntegralDomain R] → SurjVal pRℕ∪∞
v
a6p3: R
a6p3
>
0: ?m.34415
0
lemma
Warning: declaration uses 'sorry'
{
p: R
p
:
R: Type u
R
} (evr :
EnatValRing: {R : Type ?u.34541} → R[inst : IntegralDomain R] → Type ?u.34541
EnatValRing
p: R
p
) (e :
ValidModel: (R : Type ?u.34549) → [inst : IntegralDomain R] → Type ?u.34549
ValidModel
R: Type u
R
) :
cubic_has_triple_root: {R : Type ?u.34554} → [inst : IntegralDomain R] → {p : R} → EnatValRing pValidModel RProp
cubic_has_triple_root
evr e
cubic_triple_root_is_zero: {R : Type ?u.34567} → [inst : IntegralDomain R] → {p : R} → EnatValRing pValidModel RProp
cubic_triple_root_is_zero
evr (
move_cubic_triple_root_to_origin_iso: {R : Type ?u.34574} → [inst : IntegralDomain R] → {p : R} → EnatValRing pValidModel RValidModel R
move_cubic_triple_root_to_origin_iso
evr e) :=
sorry: ?m.34587
sorry
end cubic end ValidModel